Textbook Standard Quantum Mechanics StdQM for an atomic system with $N$ electrons is formulated in terms of a wave function
- $\Psi (x_1,...,x_N)$
depending on $N$ 3d spatial coordinates $x_1,...,x_N$ ranging over $N$ copies of the same physical 3d Euclidean space $\Re^3$, altogether forming a $3N$ dimensional Euclidean space $\Re^{3N}=\Re^3\times\Re^3\times....\times\Re^3$ referred to as configuration space. The wave function satisfies Schrödinger's Equation SE, which is a linear partial differential equation over configuration space.
SE was first formulated by Schrödinger for the H atom with $N=1$ in 1926, in which case configuration space $\Re^{3N}$ is identified with physical 3d Euclidean space $\Re^3$ and $\Psi^2(x)$ with $x\in\Re^3$ represents electron charge density of clear physical meaning.
But in the generalisation to $N>1$ in StdQM, which quickly followed with assistance of Bohr-Born-Heisenberg, the meaning of $\Psi (x_1,...,x_N)$ defined over configuration space is not clear and in fact has been the subject of intense debate for 100 years without ever any consensus being reached. Basic questions are:
- What is the physical meaning of SE?
- What is the physical meaning of $\Psi (x_1,...x_N)$?
- What is the meaning of the coordinates $x_1,....,x_N$?
- What is the physical meaning of configuration and configuration space?
- Does $x_i\in\Re^3$ somehow represent electron $i$ with $i=1,...,N$?
- If so, does $x_i$ represent physical presence?
- What does labelling of identical electrons mean?
- What does imposed anti-symmetry of $\Psi (x_1,...x_N)$ mean?
- What does exchange and correlation of identical electrons mean?
The textbook answer to 2 is:
- $\Psi^2(x_1,...,x_N)$ represents "all there is to know" about an atomic system.
- "All there is to know" does not include actual states of the system, but is reduced to "outcomes of experiments".
- $\Psi^2(x_1,...,x_N)$ is a "probability density of electron configurations".
The only help you get to understand textbook answers 1-9 is that any form of answer in terms of classical continuum physics, is wrong.
RealQM is an alternative to StdQM formulated in terms of classical continuum physics, which can be understood as such.

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