Quantum Chemistry 9.5 - Antisymmetry Principle

Short lecture on the antisymmetry principle for electrons.

The wavefunction of any atom or molecule must switch sign when two electrons are exchanged. This anti-symmetry principle results in a total wavefunction which is a Slater determinant. This is the physical origin of the Pauli exclusion principle, which makes the wavefunction go to zero when two electrons are placed in the same spin orbital.

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[mortin]

You have summarized 4 hours of class in 5 minutes. You are the best. I wish my quantum physics teachers would start explaining things this simple hahaha

[岡安一壽-gy]

Unfortunately, in general, neither symmetric nor anti-symmetric wavefunctions can be said to be eigenfunctions of the Hamiltonian.
The wave function for an electron in a hydrogen-like atom with atomic number Z in the ground state
is
RZ(r) is an eigenfunction of HZ=1/(2m)*p^2-Ze^2/(4πε0r).
But RZ(r) is not an eigenfunction of HZ'=1/(2m)*p^2-Z'e^2/(4πε0r), Z'≠Z.
Let us consider the case where a hydrogen-type atom with atomic number Z and a hydrogen-type atom with atomic number Z' are sufficiently separated from each other. And each electron in each atom is in the ground state.
The anti-symmetric wave function
is not an eigenfunction of the Hamiltonian
It should be an ironclad rule of quantum mechanics that the wave function is an eigenfunction of the Hamiltonian.

[aspie]

Thank you for the video!
@1:41 you say that wave function didn't change sign... On paper it did not, but what happens actually in reality? I kind of don't see why it should not have changed sign. You wrote the antisymmetry principle explanation above which makes me think that at 1:41 it should have changed sign..

[岡安一壽-gy]

Hello, sir ! The anti-symmetric wave function is not the eigenfunction and does not lead us the total energy. For example, please suppose the case Electron 1 is in a hydrogen atom and Electron 2 is in a helium ion He+. And the atom and the ion are far enough. The anti-symmetric wave function of the two electrons is not the eigenfunction of the system. Please calculate it. It is very easy.

[cristinaprimavera]

Really good! But what I never understand is: why wouldn't the exchange on the hartree give a negative? It's supposed to be "automatic" whenever you exchage, right?