Restrictions on Parameters for Oscillatory Solution in Restricted Domain

[kraigandrews]

Homework Statement

For the oscillatory solution (+k²) solution, suppose x is restricted to 0$\leq$x$\leq$a by requiring $\psi$(x)=0 and $\psi$(a)=0, what are the restrictions on A,B and k?

Homework Equations

given $\psi$(x)=Acos(kx)+Bsin(kx)

The Attempt at a Solution

so, I pretty just plugged in the zero values to get A must be zero, leaving only $\psi$(a)=0=Bsin(kx), which implies that B=0 and thus k can be 0 or pi, which seems to be a completely unreasonable result, so I am confused as to where I went wrong? Thanks

 

[LCKurtz]

You have 0 = sin(ka) not sin(kx). So ka can be any integer multiple of pi: k = nπ/a.