Physics GRE Discussion Forums

http://grephysics.net/ans/8677/96

ok i am totally confused with this.. if V +V' is even then eigenfunctions will be either even or odd, but then how can we say about the disappearance of the odd terms using symmetry, yosun also used symmetry arguments to solve 9677#98 http://grephysics.net/ans/9677/98, griffith has never used it explicitly, can anyone refer some notes or books for symmetry?

This problem asked for the ground state eigenfunction Psi(0)' only, not the general solution, but the ground state wavefunction (in a symmetrical V) is always even, so it can't have any odd terms in it.

As for the other problem, yes the static field perturbs the orbital, but that doesn't mean the energy necessarily changes. Further, the energy could change, but the "first order term" could still be zero. The only way to do that problem is to directly apply the perturbation theory formula for the first order correction, which isn't hard... but many people wouldn't learn that before taking the GRE, and you'd still have to remember the form of the ground state of hydrogen has no angular dependence.