Show that the wave function v (x, t) = [(Aeika + Be-ikx)e-iEt/h -a/2 x a/2 0...

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Show that the wave function v (x, t) = [(Aeika + Be-ikx)e-iEt/h -a/2 ≤x≤ a/2 0 otherwise = 0 in the region -a/2 ≤ x ≤a/2. (2) satisfies the Schroedinger equation with V(x) Suppose that you want (x, t) to be the wave function describing a particle that is free (with V = 0) in the region -a/2 ≤ x ≤a/2, but with V = ∞ everywhere else. In this case, the probability of finding the particle outside the "box" from -a/2 ≤ x ≤ a/2 must be zero. For what values of k will the wave function be continuous at x = ±a/2? Show that the wave function v (x, t) = [(Aeika + Be-ikx)e-iEt/h -a/2 ≤x≤ a/2 0 otherwise = 0 in the region -a/2 ≤ x ≤a/2. (2) satisfies the Schroedinger equation with V(x) Suppose that you want (x, t) to be the wave function describing a particle that is free (with V = 0) in the region -a/2 ≤ x ≤a/2, but with V = ∞ everywhere else. In this case, the probability of finding the particle outside the "box" from -a/2 ≤ x ≤ a/2 must be zero. For what values of k will the wave function be continuous at x = ±a/2?