Use the eigenfunction (x) = Ae +ikx + Be ikx rather than (x) = A

Use the eigenfunction ψ (x) = A′e^+ikx + B′e^−ikx rather than ψ (x) = A sin kx + B cos kx to apply the boundary conditions for the particle in the box.

a. How do the boundary conditions restrict the acceptable choices for A′ and B′ and for k?

b. Do these two functions give different probability densities if each is normalized?