Homework 1:
due on Sep. 5th
1. Based on Planck formula derive the Stefan-Boltzman law (the total
energy density = T 4 and the expression of ) and the Rayleigh-Jeans
formula of radiation.
2. Derive Compton formula: f i =
h
(1 cos ) by using both energy
me
Homework 2:
1.
due on Sep. 15th
Based on the wave function representation relation between in the
configuration space and momentum space, show that
( p, t ) dp = 1 .
2
2.
Show p = p if p = *( x, t )(i
*
3.
Textbook Problem 1.3.
4.
Gaussian and Square wav
Homework 6:
1. Textbook 2.14,
2. Textbook 2.17
3. Textbook 2.19
4. Textbook 2.21
5. Based upon we discussed in the class about the spreading of wave packet with time,
determine precisely how the wave packet corresponding to free particle, with an initial
Homework 8:
1. Textbook 2.38,
2. Textbook 2.46
3. Textbook 2.49
4. Consider a particle of mass subject to the potential V ( x) = for x 0 and
V ( x) = V0 ( x a) for x > 0 where V0 > 0. Discuss the existence of bound states in
terms of the size of a (a > 0)
PHY-4604 Final Exam: Fall 2006
(Solve at least 4 from these 5 problems)
Name_
Panther ID _
1. The operators associated with the radial component of the momentum pr and the radial
coordinator r is denoted by pr and r , respectively. Their action on a radia
Quantum Mechanics 2nd Exam: Solutions (2007 fall)
1. For a particle moving under a one-dimensional potential V(x), show that any two
bounded states 1 and 2 are orthogonal, based on the time-independent Schrdinger
equation.
Solutions:
If 1 and 2 are two bo
Quantum Mechanics I: 1st Exam (Fall 2007)
Name_, Panther ID _
1. If xp = /2 where (x) 2 =< x 2 > < x > 2 and (p ) 2 =< p 2 > < p > 2 but <x> = <p> = 0,
show that the minimum energy of a quantum harmonic oscillator is
Hamiltonian is H =
/2, if the
p 2 m 2
Homework 8
ADDITIONAL PROBLEM SOLUTION:
The Schrdinger equation is
2
d2
V0 ( x a ) = E
2m dx 2
For a bound state, E < 0, so that we assume that
= 2mE /
and the Schrdinger equation becomes
" 2 +
2mV0
2
( x a ) = 0 -(1)
The jump condition at x = a is gi
3. One major difference between classical and quantum mechanics on a harmonic
oscillator is that in quantum mechanics you may find probability of the particle
until x , while in classical mechanics the particle can only be in so-called
1
classical range x
Homework 5:
due on Oct. 13th
1. Textbook 2.10
2. Textbook 2.12
3. One major difference between classical and quantum mechanics on a harmonic
oscillator is that in quantum mechanics you may find probability of the particle
until x , while in classical mech