Ground State of Quantum System: l=0?

[lion8172]

ground states

Homework Statement

Is it generally true that the ground state of a given quantum system corresponds to the lowest quantum numbers? For instance, is it generally true that the ground state of a system governed by a radial potential always corresponds to l=0? If not, how do we know, in particular, that the ground state of the finite, 3-D potential well corresponds to l=0? Griffiths seems to implicitly assume this fact in one of his problems (4.9): "Find the ground state (of the 3-D finite spherical well) by solving the radial equation with l=0."

Homework Equations

The Attempt at a Solution

 

[Dr Transport]

Here is a hint, $l = 0$ corresponds to a spherical configuration, which is usually the lowest eneergy state.