The deeper the finite well, the more states it holds. In fact, a new state, the nth, is ad...

The deeper the finite well, the more states it holds. In fact, a new state, the nth, is added when the well's depth

U0 reaches h2(n-l)2/8mL2. (a) Argue that this should be the case based only on k=  the shape of the wave inside, and the degree of penetration of the classically forbidden region expected for a state whose energy E is only negligibly below U0, (b) How many states would be found up to this same "height" in an infinite well.

Exercises 38-41 refer to a particle of mass m trapped in a half-infinite well, with potential energy given by