Short lecture on Hartree-products of 1-electron spin orbitals.

A molecular system of N-electrons has a wavefunction which depends on all N spin coordinates (omega1 - omegaN) and 3N spatial coordinates [(x1, y1, z1) - (xN, yN, zN)]. The simplest way to approximate the form of such an N-electron wavefunction is as a Hartree product of N one-electron spin orbitals. In an approximate system where electrons are independent (i.e. they don't repel one another) this is an exact solution. In such an uncorrelated system the total probability density function is a product of the probability density function of each electron's spin orbital. The primary problem with Hartree products are that we know exactly which electron is in which spin-orbital, and thus the electrons are "distinguishable".

Notes Slide: https://i.imgur.com/mzM31ja.png

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