Assume a free particle, V=0, in a infinite potential square well between -L/2 and L/2
solve for the wave function for this particle.
Time independent schrodinger equation
The Attempt at a Solution
After arriving at the second order differential equation, I get a general solution of
ψ=Acos(kx) + Bsin(kx)
How do I go on to solve for A, B and k?
I've plugged in the boundary conditions, but the solution is still quite indeterminate.
I have to assume A=0, then ψ=Bsin(2n∏x/L)
however, if I assume B=0, I get ψ=Acos([2n+1]∏x/L)
which is correct?
I do need to pick one before going onto normalising right?