- #1
ani4physics
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Hi all. I have a question that I am thinking about for a couple of days. Let's consider the time-independent Schroedinger equation for a molecule:
H0 [psi> = E0 [psi>
Now, we know that the unperturbed Hamiltonian consist of electronic kinetic energy operator, electron-electron repulsion operator, electron-nuclear attraction operator, and nuclear-nuclear repulsion operator (Within the Born-Oppenheimer approximation).
If we differentiate both sides of the equation with respect to the coordinate of electron i, then we we need to consider only the gradients of electronic kinetic energy operator, electron-electron repulsion operator, electron-nuclear attraction operator, and the wave function.
My question is: Is the gradient of the electronic KE operator with respect to coordinate of electron i = 0?
Please let me know. Thanks.
H0 [psi> = E0 [psi>
Now, we know that the unperturbed Hamiltonian consist of electronic kinetic energy operator, electron-electron repulsion operator, electron-nuclear attraction operator, and nuclear-nuclear repulsion operator (Within the Born-Oppenheimer approximation).
If we differentiate both sides of the equation with respect to the coordinate of electron i, then we we need to consider only the gradients of electronic kinetic energy operator, electron-electron repulsion operator, electron-nuclear attraction operator, and the wave function.
My question is: Is the gradient of the electronic KE operator with respect to coordinate of electron i = 0?
Please let me know. Thanks.