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We first have to serparate the TISE for a central potential into two parts using separation of variables (i.e into and R(r) and Y(theta, phi). Then we take the total differential equation in R(r) and substitute R(r) = f(r)/r and get:

-(hbar^2)/2m * (d^2)f/(dr^2) + (V + c/2m(r^2))f = Ef

where c =l(l+1) where l is the angular momentum quantum no. all the mathematical derivations I can do fine.

The question notes that the equation is exactly the same form as the 1-d TISE with V replaced by V +c/2m(r^2). It then asks if we can conclude that the spectrum is the same as for the 1-d problem.

I'm a bit stumped with this. It seems obvious that if you include another term in the potential of a different form, then the energy levels should change (except for l=0), but presumably they want something better than this. Any suggestions would be greatly appreciated.

Sachi