Hi. I'm confused about degeneracy in I-D As far as I understand it ( and please tell me if i'm wrong ) ; a free particle is doubly degenerate with a continuous energy spectrum with eigenfunctions eikx and e-ikx. A particle on a ring in I-D is doubly degenerate but this time the energy is quantized. My main question concerns a particle in a 1-D infinite well with infinite walls at x=0 and x=a. The eigenfunction is given by ψ = sin (nπx/a) where n = 1,2,3,.... These eigenfunctions are non-degenerate as n only takes positive values but sin kx can be written as sin kx = ( eikx - e-ikx) / 2i which is a superposition of 2 waves travelling in opposite directions. Would this not make the particle in a box doubly degenerate ?