Thank you for replying.
So for harmonic oscillator, all dimensions are separable (H = Hx+Hy+Hz), does it depend on dimensionality? Even for one-dimensional harmonic oscillator, we can use raising and lowering operators.
Thanks
In Griffith and Shankar, the raising and lowering operator seem to appear from nowhere, but it seems really elegant.
Where do they come from, is it some corollary from certain mathematical structure?
Can anyone give a brief explanation?
Thank you fore replying.
How should I reprent ## L_z ##? is it ## XP_y - YP_x ##? Get r in spherical coordinate using raising and lowering operator and projection z axis? seems like a lot of work.
Homework Statement
Homework EquationsThe Attempt at a Solution
I suppose to determine if a hamiltonian is rotational invariant, we check if [H(1),L^2], however, I am not sure how to do it if the hamiltonian is operate on a two particle wave function.
Is it just to evaluate [S1z Z2 +S2z Z1...