Important Historical Point 1926: Schrödinger Tragedy

This is a comment to the previous post concerning the basic new problem confronting physicists in 1926 of generalising Schrödinger's equation for the Hydrogen atom with one electron, to atoms with $N>1$ electrons. Let us recall the account of this moment in the book The Stability of Matter in Quantum Mechanics by Lieb and Seiringer (2010): 

• An important historical point is to be noted here. 
• It might have been thought that the correct generalization for $N$ particles is to use 
• $N$ functions of one variable         (1) 
• instead of 
• one function of $N$ variables         (2). 
• Such a "wrong turn" did not happen historically, which is, after all, remarkable.

All the experience from the amazingly successful continuum mechanics of matter and electromagnetics in 3 space dimension (3-d) of classical physics, would point to the option (1) as $N$ one-electron (complex-valued) functions $\psi_1(x)$, $\psi_2(x)$,...$\psi_N(x)$ depending on a common 3-d variable $x$. This is the Ansatz of Real Quantum Mechanics RealQM as the "wrong turn", which was explored only recently. RealQM is a non-linear system in 3-d.

But all this experience was thrown overboard in 1926 when physics history instead took a leap into the completely unknown territory of option (2), as one N-electron (complex-valued) function $\psi (x_1, x_2,...,x_N)$ depending on $N$ 3d spatial coordinates $x_1$, $x_2$,...,$x_N$, altogether $3N$ spatial variables, to form the Schrödinger equation of Quantum Mechanics here referred to as Standard QM or StdQM,  as a linear equation in 3N-d. 

The natural option (1) of deterministic continuum physics as ontology as real physics, was thus discarded in favour of option (2) as a new form of physics as epistemology without physical meaning.

Remarkable, or maybe not at all remarkable because (2) was very easy as a purely formal mathematical generalisation, which could be done with a stroke of the pen. As easy as formally generalising from one spatial dimension to many dimensions in a Calculus course. To realise (1) was less obvious and so the ease of a formal mathematical generalisation as StdQM took over the whole scene into our days.

Today RealQM offers an alternative to StdQM. RealQM is a computable model as real physics, while StdQM is an uncomputable model without real physical meaning. 

Over the years reduced versions StdQM have been attempted with wave functions restricted to be sums of  products of one-electron charge densities $\psi_i(x_i)$ with global support as Hartree-Fock models.

Density Functional Theory DFT is a further reduction into a single charge density $\psi (x)$ representing the collective charge density of all electrons. Hartree-Fock and DFT have delivered results for atoms, but less so for dynamics of molecules. 

RealQM takes the form of a free boundary problem for a system of one-electron wave functions with non-overlapping supports, each satisfying a homogeneous Neumann condition on the boundary of its support, and meeting on a free boundary with continuity of charge density. RealQM can be used for complex molecules in dynamics of molecules as chemistry. Ready to give RealQM a try?