Consider a particle with mass m, described by the following potential:

Question

V (x) = ∞ for x ≤ 0
A for 0 < x < a
B for x ≥ a
Discuss the possibility of bound states for such a potential.
(a) Provide the energy of the two lowest energy states for the case B = ∞. (The prefactor is either known or needs to be derived.)
(b) How many bound states do you expect for A > B?
(c) For the case A < B provide the general solutions for the wave function in the two relevant regions and discuss the boundary conditions.
(d) Discuss the required steps to decide whether the case A < B yields a bound state. (An exact formulation of the equations is possible, but not required.)