A particle of mass m with energy E < 0 is trapped in the following potential:

(a) Explain why the solution to the time-independent Schrodinger equation in Region I must be _I = 0.

(b) Show that _II = Bcos(k₀x)+Csin(k₀x) is a solution of the time-independent Schrodinger equation in Region II and so derive an expression for k₀ in terms of V₀ and E.

(c) Explain why the constant B has the value B = 0 for a particle in this potential.

(d) The general solution of the time-independent Schrodinger equation in Region III is _III = Ae^x + A'e^x , where is a real, positive constant. Explain why A' = 0 for a particle in this potential.

(e) State 3 ways in which the predictions of quantum mechanics differ from the predictions of classical physics for the behaviour of a particle in this potential.

(f) Discuss whether, in general, there are any observable effects due to the existence of wave functions with 0 in regions where the potential energy exceeds the particle energy.