Wavefunction Degeneracy in Spherically Symmetric Infinite Well Potential

[Qbit42]

Homework Statement

The radial portion of the wavefunction of a particle contained in a spherically symmetric infinite well potential (ie U= infinite outside a certain radius "a" and 0 inside the radius) is given by the spherical Bessel functions.

$$J_{l}(kr) = (\frac{-r}{k})^{l}(\frac{1}{r}\frac{d}{dr})^{l}\frac{Sin(kr)}{kr}$$

I need to answer various questions for wavefunctions of different l values. One is the degeneracy of the state. For all of the l values in question (0-3) I get energy as a function of only 1 quantum number (n). This means to me that each state is not degenerate. However if none of the states are degenerate then the problem seems kinda simple. So my question is this, Do you consider degeneracy of each individual state by looking at the individual quantum numbers that specifically show up in the energy relation for that state or do I need to account for the l value of the wavefunction somehow?

 

[zhermes]

If 'l' does not appear in the equation for energy, that means that all of the values of 'l' are degenerate. That's basically the definition of degeneracy.