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**1. Apply a magnetic field B to a hydrogen like atom. This gives rise to an additional potential energy term of mu_b*B*L_z/hbar**

a) Show that the eigenfunction PSI_nlm is still an eigenfunction in the presence of the magnetic field

b) Show that the eigenvalues are E_n + m*mu_b*B

a) Show that the eigenfunction PSI_nlm is still an eigenfunction in the presence of the magnetic field

b) Show that the eigenvalues are E_n + m*mu_b*B

How do you show that the eigenfunction remains?