# Quantum Physics I PHY471, Fall
1999

# Homework set
8

# Due Monday,
11/01/1999

#

## 1.
[3 pt] Ohanian
#15, p. 94

## 2.
[1+1+2+2+2+2] Unbound states of the finite square well

Consider the unbound states (*E>0*) of the finite square well . For a wave incident from the left, the solution to the
Schrödinger equation can be written as .

a) Determine
*k* and *l*.

b) Write
down equations for all four boundary conditions for this problem.

c) Use
the boundary conditions at *x=+L* to
express *C* in terms of *F* and to express *D* in terms of *F*.

d) Use
your results from c) and the boundary conditions at *x=-L* to eliminate *A* and
to show that B can be expressed in terms of F as with .

e) Plot
the transmission coefficient versus energy over a
suitable range.

f)
For which values of the energy is the transmission coefficient
equal to 1?

## 3.
[1+2+2+1+1] Unbound states of the square
potential barrier

Consider a particle with mass *m* and energy *E>V*_{0} incident from the left on a potential .

a)
Write down the solution of Schrödinger’s equation for each
region.

b)
State the boundary conditions that apply and obtain a
sufficient number of equations to determine all unknown constants.

c)
Solve for the transmission coefficient and plot it versus
energy over a suitable range.

d)
For which values of the energy is the transmission coefficient
equal to 1?

e) Which
value does the transmission coefficient approach for *E>>V*_{0}?