# Quantum Physics I PHY471, Fall
1999

# Homework set
4

# Due Monday,
9/27/1999

#

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

## 1.
[2+2 pt] Gaussian
wavepackets and expectation values

Ohanian, #2.15, p. 55

## 2.
[1+1+1+1+1 pt]
Free particle with a wavefunction

Ohanian, #2.16, p. 55

## 3.
[1+1+1+1+1+2+2
pt] Free particle with a different wavefunction

Consider the a wavefunction similar to the one in set 2,
problem 2,

a) Determine
the constant *A* such that the
wavefunction Y(x,0) is normalized.

b) What
is the probability for finding the particle in the interval ?

c) What
is the momentum amplitude for the wavefunction?

d) For
what value of the momentum is the momentum probability maximum?

e) What
is the probability for finding the momentum in an interval *dp* around ?

f)
Evaluate the uncertainty .

g) Evaluate
the uncertainty .

## 4.
[2 pt] Classical
quantities in quantum mechanics: velocity and momentum

Ohanian, #2.23, p. 56