1.  Is the electric dipole transition from 1 to 2s> in hydrogen-like systems allowed? Suppose, you have a collection of hydrogen atoms in the 1s> state. You want to get the hydrogen atoms in the 2s> state for some experiment. Degeneracies of electronic states of various and have been removed by placing these atoms in a strong magnetic field. To excite these hydrogen-like atoms, you have a light source of variable frequency which is powerful enough to cause just the first-order transitions. How will you force the hydrogen atoms to come to the 2> state?
2. The potential energy of the hydrogen-like system is central-field or spherically symmetric type, viz. V=-Zefir, where is the distance of the electron from the nucleus. This form of the potential gives rise to the wavefunctions in the form = R ...), where Reis the associated Laguerre polynomial and Y. is the spherical harmonics. Suppose we replace the Coulombic form of the potential energy by a more general spherically symmetric function V = Vr). What changes would take place in the function ...? To what extent would the quantum number. I and mn remain valid?