Question:
Does the angular momentum operator commute with the Hamilionian in this asymmetric potential?
Solution:
Yes. The same reasoning applies just as question 7 does.
Turn out I am wrong - it commutes only with $ L_3 $.
The expression I used in question 7 assumes all coefficients are the same, but this one isn't. Some terms may not cancel.
Does the angular momentum operator commute with the Hamilionian in this asymmetric potential?
Solution:
Yes. The same reasoning applies just as question 7 does.
Turn out I am wrong - it commutes only with $ L_3 $.
The expression I used in question 7 assumes all coefficients are the same, but this one isn't. Some terms may not cancel.
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