RealQM for Nucleus

Here is a new article in the series on RealQM: 

• RealQM: Nucleus

The idea is to view an atomic nucleus to be composed in the same way as an atom with a switch of roles between electron and proton, thus with a collection of protons as charge densities around a pointlike negative charge. Such a nucleus is held together by Coulomb attraction from the negative charge overcoming Coulomb repulsion between protons. 

What Does the Schrödinger's Equation Say?

Nobel Laureate in Physics Gerhard t' Hooft is not happy with the prime jewel of modern physics in the form of Schrödinger's Equation SE as expressed in Un Unorthodox View on Quantum Mechanics:

• We know very well how to use the equation. The properties of atoms, molecules, elementary particles and the forces between all of these can be derived with perplexing accuracy using it. The way the equation is used is nothing to complain about, but what exactly does it say?
• What do these wave functions represent? In particular the ones that are not asso- ciated to photons (the energy packets of the electromagnetic field, which we think we understand very well). 
• What do those waves stand for that are associated to electrons, or other elementary particles, or even molecules and larger things, including cats, and eventually, physicists? What happens to its wave function when you actually observe a particle?
• Almost a full century has passed since the equation was written down, and fierce discussions have been held, quite a few standpoints were vigorously defended and equally vigorously attacked. We still do not know what or whom to believe, but it still goes on, while others get irritated by all this display of impotence. 
• Why is it that we still do not agree? I think I know the answers, but almost everyone disagrees with me.
• Not only may quantum mechanics be a description of the sub-microscopic world that is profoundly different from what is often asserted, particularly concerning 'what is really going on', but questions such as these may well be essential for finding new ways of constructing models beyond what is now called the Standard Model of the sub-atomic particles.

t' Hooft describes modern physics in a state of stalemate, impotence and irritation and asks for new ways of constructing models. 

I will send RealQM t' Hooft RealQM and will report his reaction. 

Note that t' Hooft repeats the mantra the physicists know very well how to use SE to derive properties of atoms and molecules with perplexing accuracy... there is nothing to complain about. Yet t' Hooft does complain because he does not understand what all this highly accurate information in fact does say? 

RealQM: Helium and Orthohelium

Here is a new article about RealQM:

• Helium and Orthohelium

added to a list of articles.

RealQM: Towards Big Molecules

Here is a new article in the series on RealQM:

• RealQM: Towards Big Molecules

Philosophy of Classical Physics vs Modern Physics

Here is a new article in the series about RealQM:

• RealQM vs StdQM: Philosophy

The idea is that philosophy enters into physics when there is a need to clarify the meaning of concepts of physics. The Philosophy of Quantum Mechanics is an academic discipline itself, typically part of a department of philosophy rather than a department of physics, powered by the fact that the Quantum Mechanics is filled with contradictions and mysteries which are not part of classical physics.

 

Germany/France/Sweden: War with Russia

Sweden, France and Germany all waged wars against Russia (1700-21, June-Dec 1812, 1941-45) and lost.

It seems that this has not been forgotten by the leaderships of these countries and that time has now come to seek revanche by escalating the US proxy war in Ukraine into a full war with Russia with victory guaranteed, even if the people has not been asked if they want to send their sons to the trenches.  

To guarantee victory military budgets are quickly tripled, conscription is planned and the delivery of weapons to Ukraine will get a new boost by eliminating any range restrictions to hit Russia. Effectively, a declaration of war has been made only awaiting formal confirmation.  

Are the chances for Sweden, France and Germany really better this time? Sweden has 10.000 soldiers, France 270.000 and Germany 180.000, none with any combat experience. Russia has about 1.3 million active with combat experience and 2 million in reserve, nuclear arms more powerful than the US, and hypersonic missiles which have no defense. Russia can take out the capitals of Sweden, France and Germany in one first strike without nuclear warheads. The nuclear umbrella of France is rusty.  

These facts are hidden to the people by big media directed to send the message that like in 1914 war (now with Russia) is necessary and a victory will be quick. The defeats have not been forgotten. Karl XII, Napoleon and H are waiting to come back..it is up to the people to stop this madness…

  

RealQM: Shell Structure and Periodic Table

Here is a next article in the series on RealQM posted in recent posts:

• RealQM: Shell Structure and Periodic Table

World expert on the Periodic Table Eric Scerri has investigated to what extent the Periodic Table can be explained by StdQM and seems to say that there are pieces missing in this puzzle. The article gives a first hint into explanations based on RealQM to be complemented with more details.

 

RealQM: First Molecule

 Here is a new article in a series about RealQM

• RealQM: First Molecule He+H

The article presents a RealQM simulation of the formation from a Helium atom He and a proton H+ the molecule He+H  from a transfer of one electron from He to H+ thus combing He+ and H into the first molecule formed after Big Bang, from which H could form from dissociation of He+H. Altogether a process to form H from He with He by its stronger kernel attraction forming before H in a sea of electrons.  

RealQM models this process as endothermic requiring input of energy (from Big Bang) to position H+ close to He with the distance determined so as to arrive at a ground state energy of He+H lower than -2.500 Hartree allowing He+H to dissociate into He+ of energy -2.000 and H of -0.5. 

StdQM gives a different perspective with instead a molecule HeH+ formed in a weakly exothermic reaction with a He atom incorporating a H+ proton. 

He+H can thus serve as a test of validity of StdQM vs RealQM since they give radically different messages.

Download article and open in Acrobat to get active hyperlinks.

See also earlier post1 and post2.

Quantum Mechanics All Wrong

In the above interview of Tim Maudlin by Brian Green we hear a message that Quantum Mechanics QM  is filled with mysteries and paradoxes. That QM does not make sense. We also hear that despite this undeniable fact, QM is a theory about atomic physics with a wave function describing in principle everything that can be known about a world built from atoms although the connection between the wave function and the real world is hidden to inspection by humans. So we've gotten a lot wrong a lot about QM but Maudlin gives no hint to a more correct theory. This is a report about a theory in stagnation since 100 years. As a possible way out of stagnation take a look at RealQM.

Weak Reactivity of Gold by RealQM

 Here is a new article to the series about RealQM as an alternative to StdQM:

• Real Quantum Mechanics: Weak Reactivity of Gold

RealQM explains why Au with electron shell configuration 2+8+18+32+18+1 with 1 valence electron in a last shell outside a sphere of radius R containing all other shells, does not form a molecule Au2 by covalent bonding as a geometric effect of large R preventing electron accumulation between kernels.

RealQM explains covalent bonding of H into H2 and non-bonding of He2 in this earlier article in the series:

• Real Quantum Mechanics: Covalent Bonding. 

Download files and open in Acrobat to get active hyperlinks.

Origin of CMBR?

Here is an interesting video about the possible origin of the Cosmic Microwave Background Radiation CMBR other than an "afterglow" of a Big Bang proving the Big Bang hypothesis to be correct, as the currently most popular cosmological theory:  

The video recalls early theories about a static Universe filled with some form of interstellar dust radiating a Planck spectrum of around 2-5 Kelvin. Such a thing was detected in 1967 at 2.7 K and was then  connected to Big Bang deleting the old theories from the map. In particular the Big Bang theory claimed to resolve the mystery of the observed red-shift of galaxies increasing with distance suggesting an accelerated expansion of the Universe. 

One of the old theories was the "tired light" hypothesis presented by Zwicki in 1929 suggesting that the red-shift could be the result of a loss of energy of light passing through interstellar dust over long distance with energy scaling with frequency.  

The idea of an active interstellar dust actively radiating at 2.7 K seems more natural than that of a Big Bang "afterglow" still hanging on after 13.8 billion years. 

Zwicki's "tired light" hypothesis can be connected to some form of dark matter as source of gravitation which shows up as CMBR resulting from sucking up energy from passing light.  I have discussed dark matter in posts on Neo-Newtonian Gravitation.   

Computational vs Theoretical Mathematics in Physics

The mathematical models of physics take the form of partial differential equations like Euler's Equations for incompressible inviscid fluid flow EE, corresponding Navier-Stokes equation for viscous flow NSE and Schrödinger's equations for atoms and molecules SE. 

The task of a theoretical mathematician has been to prove by symbolic analytical techniques (i) existence, (ii) uniqueness and (ii) regularity of solutions to a given equation with data given in some large class of possible data with data including initial data, forcing and parameters like viscosity in NSE. 

The task of a computational mathematician has been to compute solutions for specific choices of data which in each specific case can answer (i)-(iii) by inspection of the computed solution. 

It has been argued that computation is not enough, even if for each specific choice of data (i)-(iii) can be answered, because only a limited number of specific choices can be inspected. The possibly very large class of data can thus never be exhausted by computation, which gives analytical symbolic mathematics a role to play by covering a large class of data.

It is natural to ask if there are examples of equations for which the class of relevant data is so small that it can be exhausted by computation. This means first that the equation cannot contain any parameter like viscosity. Are there any models of interest which are parameter free? Inspection of EE and SE shows that they are both parameter free, and so meet the requirement of Einstein of an ideal mathematical model opening to say something about the world without measuring anything. This is like learning the area of a circular disc by computation with unit radius as only input.

Solving EE computationally thus delivers the drag of a body moving through a slightly viscous fluid such as air and water at a subsonic speed with the only data being the shape of the body and not any viscosity as parameter. This limits the class of data to shapes of bodies with a limited range of shapes of interest to be covered by computation. This is all described here.

The case of SE is in its traditional form of Standard Quantum Mechanics StdQM troubled by the fact SE by its multi-dimension nature is uncomputable and so needs dimensional compression which introduces parameters. 

RealQM is different realisation of the same parameter-free Hamiltonian as StdQM into computable form without introduction of any parameter. RealQM thus expresses SE in parameter-free computable form and so opens the possibility of saying something about the atomic world without experimental input. RealQM thus computes the ground state of an atom with the only input being the number of electrons and so can exhaust the Periodic Table.      

An analytical estimate of ground state energy as the result of a longer or shorter sequence of successive bounds, can be seen as a form of symbolic computation, while a numerical computation can be seen as very long arithmetic proof.

Computation with a parameter-free mathematical model can produce a rich set of outputs from very limited structural input, which can serve as data for AI in need of rich data. Computation is then used both to produce data and to learn from data. Symbolic mathematics has an important role to set up computation.

The Clay Institute Millennium Problem on (i)-(iii) for NSE is still open in the form of symbolic mathematics with no progress reported over 25 years. Can computation get the million dollar Prize?

Covalent Bonding by RealQM

Here is the next article in a sequence of articles exhibiting the capabilities of RealQM as an alternative to StdQM as the canon of modern physics: 

• RealQM: Covalent Bonding

with earlier articles in recent posts. Download article and open in Acrobat to get hyperlinks to essential codes to run, inspect and modify.

Shut up and Calculate vs Compute, Learn and Speak

Here is a reflection connecting to the previous post on RealQM as a computable model of atoms and molecules and Mearmin's Shut up and Calculate desperate reaction to the difficulty of making sense of the theory of Standard Quantum Mechanics StdQM. 

Let us recall the following views on the divide between StdQM as the theoretical foundation of chemistry according to physicists and the theoretical chemistry actually used by chemists. 

Eberhardt 2012:

• Chemistry is a discipline of two faces, one applied and the other theoretical. The applied face focuses on the design and synthesis of molecules and solids, while the theoretical face looks for explanations of a molecule or solid’s properties.

Bader 2011:

• ....the divide that exists in chemistry between those who seek their understanding within a universe wherein the laws of physics apply and those who prefer alternative universes wherein the laws are suspended or bent to suit preconceived ideas.

Dirac 1929:

• The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation.

Dirac identifies the root cause of the divide as the impossibility of solving Schrödinger's equation of StdQM for the complex atomic systems of chemistry. If computational solution was possible there would be no divide and the whole of chemistry would be like an open book to read by computation. 

RealQM is an alternative to StdQM which is ab initio computable for the complex atomic systems of chemistry and is also understandable in the same sense as classical continuum mechanics. If RealQM indeed shows to models physics, then there is no longer any reason for a divide between theory and practice. The Shut up and Calculate can then be replaced by Compute, Learn and Speak. 

 

RealQM Article: Stability of Atoms

Here is another article in a series of articles about RealQM to be submitted:

• Real Quantum Mechanics: Stability of Atoms 

Recall the first article in the series:

• Real Quantum Mechanics: Introduction

Download file and open in Acrobat to get active hyperlinks.

RealQM Article to Submit

I am now now preparing to submit a sequence of articles about Real Quantum Mechanics to relevant journals and here is a first test to check out reaction:

• Real Quantum Mechanics

Take a look and give a comment. 

Political Role of Quantum Mechanics

The shift from the old quantum mechanics of Niels Bohr happened with Werner Heisenberg's July 1925  "Reinterpretation" article introducing a new form of matrix mechanics without Bohr's electron trajectories to form the new quantum mechanics.  

Heisenberg was a student of Max Born at the University of Göttingen with the mathematician Hilbert as world authority of mathematical physic acting as Born's mentor. Göttingen mathematical physics was an important part of the "Weimar Renaissance" during the recovery of Germany after the defeat in WWI getting momentum in 1925. 

It is thus possible to give Heisenberg's new quantum mechanics political dimensions stretching into WWII with Heisenberg as leading scientist in Germany's quest for an atomic bomb in the "Uranium Club".  

Planck had a similar role at the height of the German Empire when he in 1900 took on the responsibility to resolve the outstanding open physics problem of black-body radiation, when to avoid failing he resorted to statistics of quanta which resurfaced in Born's interpretation of Heisenbergs new quantum mechanics.

Heisenberg worked as Bohr's assistant in 1925 and Bohr invited Born to Copenhagen in 1926, and so they came to form the Bohr-Born-Heisenberg Copenhagen school setting the agenda for quantum mechanics from its beginning into our time. 

Schrödinger entered in 1926 with his equation showing to be equivalent to matrix-mechanics, but Schrödinger did not accept the Copenhagen Interpretation and so left the field to come back only in 1954 to discover that BBH still controlled the scene. 

After WWII the US took over quantum mechanics still in the spirit of BBH.

All physicists of today say that following the idea of the mathematician von Neumann that the wave function of quantum mechanics lives in a Hilbert space of infinite dimension and most physicists will confess to the Copenhagen Interpretation even if its meaning is unclear. Schrödinger's request of physicality is met with "shut up and calculate". 

What do the Chinese say? Is it time for Schrödinger to come back in the form of RealQM in the "China Renaissance" that is now reshaping the world? It is not impossible since the Chinese are very clever, very organised and result oriented towards a clear plan.

ChatGPT: After completing his doctoral work in Budapest and Zurich, von Neumann spent the academic year 1926–27 at Göttingen. There he

• Studied under David Hilbert, attending Hilbert’s lectures on the mathematical foundations of quantum mechanics,

• Sat in on Max Born’s seminar on the new quantum theory, and

• Published his first quantum‐mechanical notes out of Göttingen later that year.

Issues with Standard Quantum Mechanics 1926-2026

There are basic unresolved foundational "issues" with Standard Quantum Mechanics StdQM based on Schrödinger's Equation SE, basically issues with SE: 

1. Unitary deterministic evolution of the wave function.
2. Collapse of the wave function upon observation.
3. Statistics of collapsed wave function by Born's Rule. 

There are many more issues (ontology, correlation, non-locality...) but the all connect to 1-3 in one way or the other. 

Major efforts have been made since the 1926 when Schrödinger formulated SE, to resolve the issues but there is still no resolution in sight accepted by most physicists. There are several very different proposals (Copenhagen, Many-Worlds, Bohmian Pilot Wave...) with the great variety suggesting that they are all wrong. 

The previous post exhibited the "weirdness" of SE in the sense of electrons having both separated existence in different worlds and existence in a common shared world. This is expressed in the multi-dimensional nature of the Hamiltonian $H_{weird}$ underlying SE. 

But there is a different interpretation of $H_{weird}$ named RealQM, which is not weird because the electrons in RealQM have only shared existence with the corresponding Schrödinger equation taking the form of classical continuum mechanics.  

By restricting electrons to share the same 3d world/coordinate system, all the issues troubling StdQM evaporate. RealQM comes out as a form of classical continuum mechanics without issues beyond those of classical physics. RealQM thus offers a unified continuum model including both micro and macro-scopic physics. 

It is a mystery why RealQM was not tried in 1926, since it is the most natural way of generalising Schrödinger's equation from one electron to many electrons, staying within classical continuum mechanics without all the issues of StdQM, which was Schrödinger's approach.

It seems that it was Heisenberg and Born who made history turn in the direction of StdQM and not RealQM. 

The following quotes of Heisenberg shows his ideas rooted in his matrix-mechanics as a new form of physics, which express essence of StdQM:

• What we observe is not nature itself, but nature exposed to our method of questioning.
• Not only is the Universe stranger than we think, it is stranger than we can think.
• The reality we can put into words is never reality itself.
• The atoms or elementary particles themselves are not real; they form a world of potentialities or possibilities rather than one of things or facts.
• The existing scientific concepts cover always only a very limited part of reality, and the other part that has not yet been understood is infinite.
• The ontology of materialism rested upon the illusion that the kind of existence, the direct "actuality" of the world around us, can be extrapolated into the atomic range. This extrapolation is impossible, however. 
• The conception of objective reality ... has thus evaporated ... into the transparent clarity of mathematics that represents no longer the behavior of particles but rather our knowledge of this behavior.

Born came to the help of Heisenberg with the statistical interpretation of the wave function of StdQM:

• If God has made the world a perfect mechanism, He has at least conceded so much to our imperfect intellect that in order to predict little parts of it, we need not solve innumerable differential equations, but can use dice with fair success.
• I am now convinced that theoretical physics is actually philosophy.
• The universe is not a puzzle to be solved, but a mystery to be embraced.

Bohr from his failed attempt to give physics to an atom, also jumped in to help Heisenberg in support of StdQM:

• It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we say about Nature. 
• Nothing exists until it is measured.
• Opposites are not contradictory but complementary.
• When we measure something we are forcing an undetermined, undefined world to assume an experimental value. We are not measuring the world, we are creating it.
• When it comes to atoms, language can be used only as in poetry.
• There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about Nature.

Together Bohr-Born-Heisenberg formed a very strong team setting the agenda of modern physics to be  StdQM against the will of Schrödinger who wanted something like RealQM. 

It may be that all the unresolved issues with StdQM having taken toll for 100 years finally will open for a come back of Schrödinger and RealQM.

Why Quantum Mechanics is "Weird"

All leading modern physicists agree that quantum mechanics is so "weird" or "absurd" that it cannot be understood: 

• Quantum mechanics describes nature as absurd from the point of view of common sense. And yet it fully agrees with experiment. So I hope you can accept nature as She is - absurd. (Feynman)
• I think I can safely say that nobody understands Quantum Mechanics. (Feynman)
• If quantum mechanics has not profoundly shocked you, you have not understood it yet. (Bohr)

The "weirdness" of quantum mechanics comes from its foundational principle in the form of Schrödinger's equation based on a Hamiltonian $H_{weird}$ of the following form for an atom with kernel of positive charge $Z$ at the origin of a 3d Euclidean coordinate system $R^3$ surrounded by $N=Z$ electrons labeled $i=1,2,...,N$:

• $H_{weird}= \sum_{i}(-\frac{1}{2}\Delta_i -\frac{Z}{\vert x_i\vert}) +\sum_{j<i}\frac{1}{\vert x_i-x_j\vert}$                                        

where each $x_i$ is a 3d coordinate for a separate copy of $R^3$ and $\Delta_i$ the Laplacian differential operator with respect to $x_i$. The Hamiltonian $H_{weird}$ acts on wave functions $\psi (x_1,x_2,...x_N)$ depending on $N$ 3d spatial variables $x_i$, each $x_i$ serving to represent an electron with presence over the whole of its own copy of $R^3$, thus based on electronic wave functions having global supports.

The weirdness comes from the many dimensions where each electron $i=1,...,N$ is equipped with a separate copy of $R^3$, where it is acted upon by a Laplacian differential operator $\Delta_i$ giving it kinetic energy, yet the electrons interact in a common $R^3$ by the presence of $\vert x_i-x_j\vert$ in the term representing Coulomb electronic repulsion. The electrons thus have both separated individual existence and shared existence. That is weird from classical continuum mechanics point of where a shared single physical 3d space is the only one available. With a travesty of Bohr, one could maybe say

• If from a  knowledge of classical continuum mechanics, you are not shocked by $H_{weird}$, then you have not understood classical continuum mechanics.

Quantum mechanics is thus weird unphysical because it is based on a Hamiltonian $H_{weird}$, which is weird unphysical. Of course, if you are dealing with something which is partly weird, then you have to get rid of the weirdness and keep whatever is not weird and maybe useful.  Efforts to this end e g in the form of Density Functional Theory have been made without however completely getting rid on the weirdness. RealQM is a based on $H_{weird}$ but with a new meaning which is physical and not at all weird, see this post for an intro. 

 

Physics and Mathematics of Schrödinger's Equation

The Schrödinger equation describes the ground state of the Hydrogen atom by the wave function $\Psi (x)$ with $x$ a 3d spatial variable, which minimises the total energy

• $E =E_{kin} + E_{pot}$

as the sum of 

• $E_{kin} =\frac{1}{2}\int\vert\nabla\Psi (x)\vert^2dx$     (electronic kinetic energy)
• $E_{pot} =  -\int\frac{\Psi^2(x)}{\vert x\vert}dx$              (electronic Coulomb potential energy)

under the side condition

•  $\int\Psi^2(x)dx =1.$

The model contains the following three components as functions of $x$: 

1. Distributed charge density: $\Psi^2(x)$ with unit total charge.
2. Distributed kinetic energy: $\vert\nabla\Psi (x)\vert^2$.
3. Distributed potential energy: $-\frac{\Psi^2(x)}{\vert x\vert}$.  

The solution can be computed analytically to be $\Psi (x)=\frac{1}{\sqrt{\pi}}\exp(-\vert x\vert )$. The total energy represents the ground state energy of a Hydrogen atom with kernel at $x=0$. The Coulomb potential is classical physics, while the kinetic energy is a new form of energy measured by the gradient $\nabla\Psi (x)$ as an analog to classical elastic energy. The model has a clear physical meaning and the ground state is characterised by a charge density which concentrates around the kernel paying a kinetic energy cost. 

The Schrödinger equation for the Hydrogen atom in charge density is an example of an Eulerian continuum model of the same form as the Navier-Stokes equations for fluid flow in terms of velocity and pressure as distributed functions of a 3d space coordinate, where individual particle trajectories are not followed. A major advantage of a continuum model is that it allows very efficient computation under discretisation of different spatial resolution.

Schrödinger's equation does not involve point positions of electrons, just distributed charge density, and thus has nothing to say about point positions of electron. At least this is what a mathematician would say understanding that a mathematical model does not contain more than what is put in. Even an emergent phenomenon is a consequence of input. It is not meaningful to ask about point positions of the planets in the Solar system at some given time from a model that only contains time-less orbits of the planets. 

A mathematician would add that neither can exact point position of the electron of a Hydrogen atom be determined experimentally. Wittgenstein would agree that asking about electron position does not make sense in the Schrödinger charge density model and so should not no be spoken of.  

But physicists would not hesitate to say that it is meaningful to ask about the position of the Hydrogen electron, even if it is not contained in the model and cannot be experimentally determined. A physicist would insists that Schrödinger's equation is to be viewed to be formulated in terms of a probability density of electron point position, and not charge density. 

But a probability density is not by itself any physical quantity, and is instead by physicists described as a catalog of possible electron point positions. But physics does not keep such a catalog. Changing from charge density to probability density thus turns Schrödinger's equation from being a model of physics into a model of non-physics. 

So why did physicists take this step in 1926 when seeking to give a meaning to Schrödinger's equation for the Hydrogen atom, which had shown to accurately capture the spectrum of the Hydrogen atom from electronic energies of excited states of the ground state. Schrödinger certainly viewed his equation for Hydrogen in terms of charge density and not probability density.

The switch to probability density came with an ad hoc generalisation of Schrödinger's equation for atoms with more than one electron in terms of a multi-dimensional wave function depending on $3N$ spatial variables for an atom with $N>1$ electrons. With the help of Max Born this model was given an interpretation in terms of probability density to form Standard Quantum Mechanics StdQM as the foundation of modern physics. Here Born's rule states that experimental observation of a prepared quantum state as a given linear combination of eigen-states, choses one of the eigen-states with probability measured by its coefficient in the linear combination. 

This is called collapse of the wave function and has remained a true mystery from physical point of view. The eigen-states are deterministically determined by Schrödinger's equation and so the spectrum. Statistics thus enters only in experimental observation of prepared states while the spectrum is always the same. 

This connects to the view of Bohr that the objective of StdQM is to predict outcomes of prepared experiments, not to model reality. This is mind-boggling and does not seem to make any sense. 

 

Main efforts have been made over the 100 years since 1926 to give StdQM back some physical meaning but no consensus about interpretation in terms of charge density has been reached. 

RealQM presents a new different generalisation to $N>1$ of the Schrödinger equation for $N=1$ in terms of a system of electronic non-overlapping charge densities, which keeps the physicality of the Hydrogen atom. RealQM is a continuum model in 3d with computational cost scaling linearly with $N$, compared to StdQM with exponential scaling. 

The linearity of the Schrödinger equation of StdQM invited to a mathematical analysis using the machinery of the new field of functional analysis developed by Hilbert in terms of Hilbert spaces, which von Neumann exploited in a form of axiomatic formal mathematics (in uncomputable form) with axioms without clear physical meaning.   

Mathematics can thus serve to keep physicality of quantum mechanics as in RealQM, but also by von Neumann abstraction leave physicality as in StdQM. Physics education has been locked on StdQM with all its complications from non-physicality as expressed by Nobel Laureate Murray Gell-Mann 50 years ago:

• Niels Bohr brainwashed a whole generation of theorists into thinking that the job of interpreting quantum theory was done 50 years ago.

The brainwash has continued since text-book physics still today is StdQM. Attempts have been made to give StdQM physical meaning like Many-Worlds and Bohmian Pilot Wave but are not viewed to be successful. RealQM opens a new way of thinking, which apparently has been brainwashed away for 100 years... 

Bohr quotes:

• Physics is not about how the world is, it is about what we can say about the world.
• Those who are not shocked when they first come across quantum theory cannot possibly have understood it.

Yes, it is shocking to learn that StdQM it is not about how the world is, that StdQM is non-physical. Schrödinger would have welcomed RealQM as a theory about physics, while such a thing would have shocked Bohr again...

RealQM is based on the same physics as the Hydrogen atom: Coulomb potential energy and kinetic energy. RealQM appears to be about how the microscopic world is...just like Newton's mechanics based on Newton's laws of motion appears to describe how the macroscopic world is...and RealQM connects seamlessly to Newton's mechanics in a unified continuum model.