Consider a particle in a one-dimensional box defined by V (x) = 0, a > x > 0 and V (x) = ∞, x ≥ a, x ≤ 0. Explain why each of the following un-normalized functions is or is not an acceptable wave function based on criteria such as being consistent with the boundary conditions, and with the association of ψ^* (x)ψ (x) dx with probability. All constants are nonzero.

a. A cos nπx/a + B sin n πx/a

b. C(1 – sin nπx/a)

c. C x³(x – a)

d. D(a – x)x

e. E/cos(nπ/a)