Q3. [30] A particle of energy E approaches a finite square potential well (Vo) from the left. What classical behavior can be expected when the particle encounters such a potential (shown below)? For E<Vo, solve the Schrödinger equation (show your work) and (a) plot the wave function ψ(x) and the probability distribution |ψ(x)|^2 for n = 1, 2, 3, 4, 5 (similar to those shown for an infinite square well in class). (b) Compare the lowest five energy levels of the infinite square well and that of the finite square well of the same width. [Hint: Energy levels of the infinite well were derived and plotted in class. Solve the Schrödinger equation for the finite well, apply boundary conditions, and find the energy levels. Compare the energy levels in the two cases].
V(x)
X
X = 0
X = L
Fig. Finite square well potential.