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Chapter 5: Q 9CQ (page 186)

A half-infinite well has an infinitely high wall at the origin and one of finite height U0 at x= L . Like the finite well, the number of allowed states is limited. Assume that it has two states, of energy E1 and E2 , where E2 is not much below U0. Make a sketch of the potential energy, then add plausible sketches of the two allowed wave functions on separate horizontal axes whose heights are E1 and E2 .

Short Answer

Expert verified

E1 and E2 are two states of energy in a half-infinite square well. At a distance of L from the left wall, the right "step" has a height of U0 .

Step by step solution

01

Given data

Halfway between an infinite square well (potentials on both sides are infinite) and the finite square well lies the half-infinite square well.

02

Graph for the data

A half-infinite square well with two states of energies and E1 and E2 . Here the right "step" has a height of U0 at a distance L from the left wall. First, we will draw the potential. This is pretty straightforward. "An infinite barrier exists at the origin, followed by a finite barrier at." x= L.

Hence, E1 and E2 are two states of energy in a half-infinite square well. At a distance of L from the left wall, the right "step" has a height of U0 .

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