Brief Quantum Story

The first form of the Schrödinger equation presented by Schrödinger in 1926  offered a mathematical model of the Hydrogen atom with one electron in the form of a linear wave equation of classical continuum mechanical form in terms of a (complex valued) wave function $\psi (x,t)$ depending on a 3d space coordinate $x$ and a time coordinate $t$ with $\vert\psi (x,t)\vert^2$ representing charge density at $(x,t)$ with total unit electron charge. The corresponding classical eigenvalue problem with discrete eigenvalues showed to fit exactly with the observed discrete spectrum of Hydrogen. 

The success was immense and Schrödinger rocketed to fame by giving birth to a new form physics of atoms to be named Quantum Mechanics QM, but it was not Schrödinger who coined the concept of quantum, and in fact he disliked it from the bottom of his heart:

• If all this damned quantum jumping were really here to stay, I should be sorry I ever got involved with quantum theory.

Recall from recent posts that that the quantum was the result of desperate actions by first Planck in 1905 introducing a quantum of energy $h\nu$ associated with radiation of frequency $\nu$ with $h$ a very small constant indicating that a quantum of energy is a very small quantity. Einstein followed in 1905 by suggesting that light of frequency $\nu$ could be thought of (heuristically only!) as a stream of light particles or photons each photon carrying exactly one quantum of energy $h\nu$. Vivid fantasy.

Then 20 years passed with the idea of the quantum of energy $h\nu$ kept as a form of easy fix to explain blackbody radiation and photoelectricity believed to be impossible within classical continuum physics. 

Schrödinger gave his revolutionary Hydrogen article the title "Quantisation as Eigenvalue Problem" thus connecting back to the a concept of "quantisation" suggested earlier by Bohr and de Broglie and coming out in Heisenberg's matrix mechanics, which he now reformulated as an eigenvalue problem of the form of classical continuum physics. Schrödinger's goal was to show that the new quantum mechanics of atoms in fact could take the form of classical continuum mechanics. Schrödinger never gave up that goal but could only reach it in the case of the Hydrogen atom with one electron, since already the Helium atom with two electrons appeared to require a new model outside classical continuum mechanics, and so Schrödinger left QM in 1928 disgusted, to let it be formed by Bohr-Heisenberg as a fundamentally new form of physics as QM, which has come to serve as the foundation of modern physics, without Schrödinger the founder of QM 

But back to Schrödinger's equation for the Hydrogen atom, which does not ask for any quantum of energy $h\nu$ carried by a photon. It is a classical continuum physics eigenvalue problem with discrete spectrum of eigenvalues $E_1<E_2<E_3,...$ representing energies of excited states staring from a ground state energy $E_1$. Differences of eigenvalues $E_n-E_m$ with $E_n>E_m$ match with frequencies $\nu$ in the observed spectrum of Hydrogen under scaling with a certain constant $h$. There is here only a superficial connection between a classical continuum physics eigenvalue problem and the new concept of quantum of energy scaling with frequency $\nu$.  Schrödinger managed to turn quantisation into a classical eigenvalue problem. 

Once the Hydrogen atom was secured within classical continuum physics without the real need of any quantum of energy $h\nu$, which he disliked so much, Schrödinger took on the Helium atom with two electrons. And this is where history took a turn with far-reaching consequences into our time. Instead of staying within classical continuum physics, Schrödinger and everyone else took the easy way out by generalising from one electron to many electrons by a purely formal procedure leaving out physics. For some reason, Schrödinger and everyone else missed the possibility demonstrated in Real Quantum Mechanics RealQM of staying within classical continuum physics without need for any quantum of energy. 

The result of taking the easy formal route when generalising Schrödinger's equation from one electron to many and so form StdQM as the textbook version of QM today, is that "nobody understands QM", simply because the easy formal route does not make sense from physical point of view. What does not make sense cannot be understood, and if something cannot be understood, it is because it does not make sense. 

What about giving RealQM a try, if you want to understand QM? RealQM offers an understanding of blackbody radiation and photoelectric effect with a frame of classical continuum physics!