StdQM as Voodoo Mechanics

Textbook Standard Quantum Mechanics StdQM can be viewed to be a form of voodoo physics in the sense that symbolic formalism has taken over the physical realism of classical physics. This is expressed by the icon of StdQM in the form of a (real or complex-valued) wave function $\Psi (x_1,...,x_N)$ for an atomic system with $N$ electrons depending on $N$ 3d spatial variables $x_i$ in 3d Euclidean space $\Re^3$ for $i=1,...,N$, each variable somehow associated with an electron. We can collect the spatial variables $x_i$ into $x=(x_1,...,x_N)\in\Re^{3N}$ and thus exhibit $\Psi (x)$ as depending on a coordinate $x$ in $3N$ dimensional Euclidean space. 

For example, for a single $H_2O$ molecule, we  have $N=10$ and so representation of the values of $\Psi (x)$ for a very modest resolution of 100 in each $\Re$, would require specification of $10^{60}$ numbers which compares with the number of atoms in the Solar system 

We understand that $\Psi (x)$ from both physical and computational point of view is a disaster and so represents voodoo science as purely formalistic science. Recall that a voodoo magician puts a stick through a doll representing your enemy and asks for your money to give result. A physicist speaks about $\Psi (x)$ with $x\in\Re^{3N}$.  

In any case $\Psi (x)$ is expected to satisfy a Schrödinger Equation SE and so describe some atom physics. In SE the 3d variables $x_i$ have a double role of both representing presence of electrons around coordinate $x_i$ in a common physical $\Re^3$, and also the spread of each electron in each private $\Re^3$ as given by the presence of a Laplacian acting with respect to $x_i$. The construction is indeed very strange. 

In any case, to get a computable model the wave function is dimensionally reduced to consist of sums of products of wave functions $\Psi_i(x_i)$ depending on only one spatial variable $x_i$, typically products with two factors, which are symmetrized into (with $i\neq j$):

•   $\Psi(x_i,x_j)=\Psi_i(x_i)\Psi_j(x_j)+\Psi_i(x_j)\Psi_j(x_i)$

with the property that $\Psi (x_i,x_j)=\Psi (x_j,x_i)$ deemed to be necessary because 

• electrons are indistinguishable.

The result is that total energy as 

• $\int\Psi H\Psi dx$ 

with a $H$ a Hamiltonian, will contain contributions from 

• $\int\Psi_i(x_i)\Psi_j(x_i)H\Psi_j(x_i)\Psi_j(x_i)dx$ 

as exchange terms characteristic of StdQM. A major mystery of StdQM is the physical meaning of the exchange terms, which have no counterparts in classical physics. 

In RealQM physical $\Re^3$ is subdivided into domains $\Omega_i$ acting as support for electronic wave function $\Psi_i(x)$ with $x\in\Re^3$, in which case the exchange terms vanish, and $\Psi (x)=\sum_i\Psi_i(x)$ with $x\in\Re^3$ making $\Psi (x)$ computable.

The generalisation of SE from $N=1$ to $N>1$ was made on purely formalistic grounds and it became necessary to introduce physics by dimensional reduction. RealQM appears as a natural model based on non-overlapping one-electron charge densities, which can be seen as an elaboration of Density Functional Theory DFT as extreme reduction into a single common electron density. RealQM avoids the complication of the exchange terms appearing in DFT.