Having trouble as to why for Sin j cannot equal 0. Since Sin (0) = 0 and Sin (2pi)= 0, doesn't this fit the boundary condition of the particle on a ring, ( the wave is cyclic)

Was wondering if this answer is correct.

Why can the particle on a ring have an energy level of 0?

The particle on a ring can have an energy state of 0, corresponding to j=0, since the only requirements for the particle on a ring are to have a integer ( the wavefunctions must repeat on successive cycles. Meaning they must have the same values at 0 and 360 degrees.) number of waves around the ring. The sine wave function is not defined at j= 0 however the cosine wave function is defined at j=0/ This ground state has the particle motionless around the ring with a constant zero amplitude. J= 0 is not degenerate since the sine function is not defined for 0.

Thanks.