Consider a particle in a one-dimensional box defined by V (x) = 0, a > x >
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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)
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