# Quantum Physics I PHY471, Fall
1999

# Homework set
6

# Due Monday, 10/18/1999

#

*Please clearly state your assumptions, number the
equations and indicate logical connections between different lines.*

## 1.
[2+2+2+2+2 pt] Infinite
square well

Consider the potential .

a) State
all applicable boundary conditions.

b) Find
the time-dependent wavefunctions of the stationary states over the region -.

c) Find
the energy eigenvalues.

d) For
the ground state, evaluate Dx and Dp according to their definitions as rms
deviation from the mean. What is the
product of Dx and Dp?

e) For
the first excited state, evaluate Dx
and Dp according to their definitions
as rms deviation from the mean. What is
the product of Dx and Dp?

## 2.
[4 pt] Orthonormality
of eigenfunctions of the infinite square well

Prove that the
eigenfunctions of the infinite square well are orthonormal (eq. (35) on page
67). Hint: You can write *sin(ax)* in as *(e*^{iax} – e^{-iax})/(2i) and then do the integral.

## 3.
[1+1+2+1+1pt] Particle
in infinite square well

Ohanian, #3.5, p. 92