Schrödinger vs Real Quantum Chemistry

Schrödinger was not happy with mainstream quantum mechanics, nor his cat.

The foundation of modern physics in the form of quantum mechanics is Schrödinger's equation formulated by Erwin Schrödinger in 1926 for the Hydrogen atom H with one electron as a partial differential equation of simple form in 3d Euclidean space with coordinate $x$ allowing analytical solution with eigenvalues in full agreement with the spectrum of H. The ground state electronic wave function as eigenfunction was given by the exponential function $\psi (x)=\frac{1}{\sqrt{\pi}}\exp(-\vert x\vert )$ decaying with distance $\vert x\vert$ from the H kernel at $x=0$ with $\psi (x)^2$ representing charge density with total charge $\int\psi(x)^2dx=1$.  

Schrödinger was very happy with his equation for the H atom since its eigenfunctions had a clear physical meaning as charge densities in a classical continuum mechanics sense. 

It remained to extend Schrödinger's equation to atoms with many electrons and this work was done in cooperation with other physicist including Born and Pauli, in the form of a purely formal trivial extension adding a new set of 3d spatial variables for each new electron into model in $3N$ dimensions for an atom with $N$ electrons to form Standard Quantum Mechanics StdQM. This development made Schrödinger very unhappy, since the eigenfunctions of the multi-dimensional model no longer had any real physical meaning, only a statistical meaning invented by Born. Schrödinger insisted that this could not be accepted but was overpowered and found no place in the further development until making a last fruitless effort in the 1950s to bring realism back to quantum mechanics. 

RealQM offers a new form of Schrödinger's equation as different generalisation of the one-electron model in the form of a system of non-overlapping charge densities with direct physical meaning. This model satisfies Schrödinger's demands of realism. 

Michel Bitbol gives in Schrödinger's Philosophy of Quantum Mechanics a detailed review of Schrödinger's successive positions from start to end, including the information that from 1928 Schrödinger resigned himself from teaching mainstream quantum mechanics. 

The lack of realism of StdQM is accepted by physicists, but poses problems for a chemist used to think of molecules as real physical structures in 3d kept together in chemical bonding. RealQM offers consolation for a chemist troubled to fit such a realist view with formalist StdQM.   

Bitbol writes:

• Pauli went as far as denouncing Schrodinger's "neurotic" regression and accusing him of entertaining the dream of a way back, back to the classical style of Newton-Maxwell, that is hopeless, off the way, bad taste and not even a lovely dream.
• Many physicists rejected Schrodinger's proposals, without even bothering go examine his arguments with any care. 
  

Can Chemistry be Reduced to Standard QM?

The mantra of modern physics is that Chemistry fundamentally is a branch of Quantum Physics based on Schrödinger's equation of Quantum Mechanics QM as Standard QM, which appears to be accepted in principle by a majority of chemists as reductionists, under the agreement that the reduction is yet to be realised, the big obstacle being that Schrödinger's equation is uncomputable.

There are some prominent chemists who have expressed clear anti-reductionist views pointing to inabilities of QM to describe fundamental aspects of chemistry:

• Hans Primas: emergence  
• Guy Woolley: molecular structure
• Norman Hunter: chemical bonds and reactivity 

and Roald Hoffman viewing chemistry as creative science beyond QM. It may be that in fact most chemists share such views and think of chemistry rather in terms of molecular structure in 3d with chemical bonds formed under chemical reactions, than as abstract StdQM.

RealQM is based on a new form of Schrödinger's equation, which has direct physical interpretation in terms of non-overlapping charge densities, closely connects to chemists conception of molecules as formed by atomic kernels surrounded by electrons carrying individuality by occupying different regions of space. RealQM thus opens to a form of Real Quantum Chemistry explored under this tag, where there is no gap between theory and chemistry reality since the Schrödinger equation of RealQM is readily computable. 

• Quantum chemistry is but a narrow subfield of theoretical chemistry and numerical quantum chemistry is nothing but a powerful tool. (Hans Primas in Chemistry, Quantum Mechanics and Reductionism).
• All that has happened (in the 20th century) is that the 19th century rupture between chemistry and physics has been patched over in framework of quantum chemistry. (Guy Woolley in Foundations of Molecular Quantum Electrodynamics)