So I am working on the problem of the particle bound to a ring of radius R. I am trying to solve it two ways, as a standing wave and as a running wave. I'm stuck right now solving for the standing wave. So far I have: ψ(x)=Asin(kx) + Bcos(kx) I know that it is periodic from 0 to 2π so if I integrate the modulus of ψ(x) squared I can set it equal to 1 and solve for A & B. So my question is this, would the B value be zero? Since it is periodic around the ring, would the only way to make cos(kx) zero be to make coefficient B zero?