PHY4605Introduction to Quantum Mechanics II
Spring 2005
Test 2 SOLUTIONS
March 9, 2005
Short Answer. Must attempt (only) 3 of 6. Circle answers to be graded.
1. Identify or short answer:
(a) Born-Oppenheimer approx. Discuss the philosophy and its implemen
PHY4605Introduction to Quantum Mechanics II
Spring 1997
Problem Set 4
Jan. 31, 2005
Due: Feb. 7, 2005
Reading: Griths, Ch. 6
1. Finite extent of proton.
The binding energy and ground state of an electron in an H-atom are normally
obtained under the assump
PHY4605Introduction to Quantum Mechanics II
Spring 2005
Problem Set 9
March 30, 2005
Due: April 6, 2005
Reading: Griths Ch. 11
1. Well . Consider a spherically symmetric at potential well,
V (r)
V0 r r0
0 r > r0
where V0 and r0 are positive real constants
PHY4605Introduction to Quantum Mechanics II
Spring 2005
Problem Set 7
Mar. 14, 2005
Due: Mar. 21, 2005
Reading: Griths, Ch. 9
1. H-atom in t-dependent electric eld. Griths, Problem 9.1
2. Exponential pulse.
An H-atom in its ground state is subjected to a
Homework 7 Solutions
1. A) The Fourier Transform of the Rectangular pulse function
0 if t >1/ 2
rect(t) = 1/ 2 if t =1/ 2.
1 if t <1/ 2
is given
Here is the Rectangular Function:
and here is the SINC(x) function:
by: where sinc( x) = sin( x) / x.
B). Th
Physics 4605, Quantum Mechanics II, Spring 2013
April 1, 2013
_
EXAM 2
Name and Signature
Please do all 3 of the problems. A total of 105 points is possible (this includes 5 bonus points). Not all
problems are worth equal number of points. Remember to wor
Physics 4605, Quantum Mechanics II, Spring 2014
February 13, 2014
_
EXAM 1
Name and Signature
Please do all 4 of the problems. Each is worth 25 points. Remember to work each problem as
fully as possible. SHOW ALL WORK as partial credit will be given.
You
Physics 4605, Quantum Mechanics II, Spring 2013
February 15, 2013
_
EXAM 1
Name and Signature
Please do all 3 of the problems. Each is worth 35 points (for a total of 105 with bonus points).
Remember to work each problem as fully as possible. SHOW ALL WOR
PHY4605Introduction to Quantum Mechanics II Spring 2005 Problem Set 6 Feb. 21, 2005 Due: Mar. 7, 2005 Reading: Griths, Ch. 7 1. Atomic congurations. Griths, Problem 5.12 2. Yukawa Hydrogen. Griths, Problem 7.14 3. Rubber band Helium. Griths, Problem 7.17
PHY4605Introduction to Quantum Mechanics II
Spring 2005
Problem Set 5
Feb. 14, 2005
Due: Feb. 21, 2005
Reading: Griths, Ch. 6,7
1. Zeeman splitting. Griths, Problem 6.23
2. Feynman-Hellman theorem. Griths, Problem 6.33
3. Variational theorem for SHO. Grit
PHY4605Introduction to Quantum Mechanics II
Spring 2004
Test 1
February 6, 2004
One formula sheet and calculator allowed, no other materials. If you cant do one
part of a problem, solve subsequent parts in terms of unknown answerdene clearly.
All parts 10
PHY4605Introduction to Quantum Mechanics II
Spring 2005
Problem Set 3
Jan. 24, 2005
Due: 31 January, 2005
Reading: PH notes
Remarks: On problem set 1 too many people had continued diculty with matrix
algebra. To solidify these crucial concepts, heres more
PHY4605Introduction to Quantum Mechanics II
Spring 2005
Problem Set 1
Jan. 5, 2005
Due: Jan. 14, 2005
Reading: PH Notes, Griths Sec. 4.4.2
1. Inhomogeneous eld
Consider a neutral spin-1/2 particle moving in a magnetic eld
B = x + (B0 + z)k
i
(a) Verify th
1
PHY4605
Problem Set 5
Solutions
1. Strong eld Zeeman Splitting. Griths Problem 6.23. The zeroth-order Bohr
energy is the same for all states, E2 = R/22 = 3.4eV. The Zeeman contribution is
2nd term in Griths Eq. 6.79, B B(m + 2ms ). The ne structure ener
PHY4605Spring 2005
Problem Set 1, Solutions
Due: Jan. 14, 2005
1. Inhomogeneous eld B = x + (B0 + z)k
i
(a)
x+0+ z
x
z
= + = 0
B =
(b) The Hamiltonian is H = 0 B = 0 [xx + (B0 + z)z ]. We can then
write the time evolution operator as
iHt
h
= exp [i(ax +
PHY4605Introduction to Quantum Mechanics II
Spring 2005
Problem Set 8
March 21, 2005
Due: Mar. 28, 2005
Reading: Griths Ch 9
1. Dipole transitions. The electric dipole approximation to a radiative transition
between states of a system of charged particles
PHY4605Introduction to Quantum Mechanics II
Spring 2005
Take-home nal exam
April 18, 2005
Due April 22, 2005 5pm
Do all problems. Open book. Do not consult with anyone else.
1. Short answer (10 pts.)
(a) Write the expression | = 1 as an explicit integral
1
PHY4605Introduction to Quantum Mechanics II
Spring 2004
Test 1 Solutions
February 6, 2004
1. Short Answer. Must attempt (only) 3 of 4. Circle answers to be graded.
(a) Explain the Einstein-Podolsky-Rosen paradox. How does the Copenhagen school of quantu
PHY4605Introduction to Quantum Mechanics II
Spring 2005
Test 1 Solutions
February 9, 2005
1. Short Answer. Must attempt (only) 3 of 4. Circle answers to be graded.
(a) Sketch an experiment to measure the Aharonov-Bohm eect, and comment
on the signicance o
PHY4605Introduction to Quantum Mechanics II
Spring 2004
Test 3 Solutions
April 16, 2004
1. Short Answer. Must attempt (only) 4 of 6. Circle answers to be graded.
(a) Using the gure sketching the wave
function of a particle with the scattering potential a)
PHY4605Introduction to Quantum Mechanics II
Spring 2004
Test 3
April 16, 2004
No materials allowed for exam. If you cant do one part of a problem, solve subsequent
parts in terms of unknown answerdene clearly. All parts 10 pts., max=70. Problem
1 required
PHY4605Introduction to Quantum Mechanics II
Spring 2004
Test 2 Solutions
March 17, 2004
1. Short Answer. Must attempt (only) 3 of 6. Circle answers to be graded.
(a) Given the exact normalized eigenfunctions n of a quantum system, Hn =
En n , prove the va