00:01
All right, so let's say we have a harmonic oscillator in three dimensions, and it has a small perturbation.
00:07
So the potential looks like this.
00:09
We have, you know, our x, y, and z terms.
00:13
So that's the isotropic part.
00:15
But then we have a lambda xy term.
00:19
And so we want to find the first and second order shifts in the energy level.
00:25
Well, the first order shift is actually the easy one.
00:27
So we'll call this, we'll write it as e1 to denote the order of this, because this is just going to be basically the original, or we're looking for the shift.
00:42
So this will be the expectation of the nth like energy state with this perturbing hamiltonian, or perturbing part.
00:51
So we'll write this as lambda xy times n.
00:57
And then of course, we have our term 1 half m omega squared here.
01:01
So this can be written as the 1 half m omega squared times xy, or the expectation of xy, like in the nth state...