Quantum Mechanics II (40454) Homework Assignment #15
Due Feb. 9 in class
Please complete the following problems found in your text:
6.13 - You need to solve 4.43(a) and (c) as part of this problem.
6.14
6.16
6.18
6.19
Midterm Exam Solutions - Quantum Mechanics II (PHYS40454)
(Dated: March 7, 2011)
PROBLEM I
a. The orthonormality is seen by
l |l =
1
2
2
ei(l l) d = l,l .
0
That the given wave functions are eigenfunction to H 0 is seen by direct insertion:
)
(
2 2
h
1
Midterm Exam - Quantum Mechanics II (PHYS40454)
(Dated: March 7, 2011)
INSTRUCTIONS: Write your NAME on the front of the blue exam booklet and
sign it.
The exam is open book; you may use your textbook, notes, homework and solution handouts, tables of inte
Midterm Exam Solutions - Quantum Mechanics II (40454)
(Dated: March 2, 2010)
PROBLEM I
a. The Hydrogen ground state wave function is
100 =
1
a3
er/a .
Then the rst-order correction to the ground state energy is easily calculated:
2
eEext
1
E1 = 100|H |1
Midterm Exam - Quantum Mechanics II (40454)
(Dated: March 2, 2010)
INSTRUCTIONS: Write your NAME on the front of the blue exam booklet and
sign it.
The exam is open book; you may use your textbook, notes, homework and solution handouts, tables of integral
Midterm Exam Solutions - Quantum Mechanics II (40454)
(Dated: March 5, 2009)
PROBLEM I
a. We take the know ground state wave function for the one-dimensional harmonic oscillator
from Griths Eqs. 2.71 and 2.85:
0 =
m
h
1/4
2 /(2 )
h
emx
.
Then the rst-orde
Midterm Exam - Quantum Mechanics II (40454)
(Dated: March 5, 2009)
INSTRUCTIONS: Write your NAME on the front of the blue exam booklet and sign it.
The exam is open book; you may use your textbook, notes, homework and solution handouts, tables of integral
Final Exam Solutions - Quantum Mechanics II (PHYS40454)
(Dated: May 9, 2011)
PROBLEM I
a. Lithium is element number 3 with electron conguration (1s)2 (2s)1 . It is therefore most reasonable
to assume that the Li-atom gives up the single 2s-electron to the
Final Exam - Quantum Mechanics II (PHYS40454)
(Dated: May 9, 2011)
INSTRUCTIONS: Write your NAME on the front of the blue exam booklet and
sign it.
The exam is open book; you may use your textbook, notes, homework and
solution handouts, tables of integral
Final Exam Solutions - Quantum Mechanics II (40454)
(Dated: May 5, 2010)
PROBLEM I
a. In two dimensions one state occupy an area of 2 /A in k -space. The k -space area with k < kF is
given by
12
2 kF ,
4
where the factor of two is due to the spin degenera
Final Exam - Quantum Mechanics II (40454)
(Dated: May 5, 2010)
INSTRUCTIONS: Write your NAME on the front of the blue exam booklet and
sign it.
The exam is open book; you may use your textbook, notes, homework and solution handouts, tables of integrals, e
Final Exam Solutions - Quantum Mechanics II (40454)
(Dated: May 4, 2009)
PROBLEM I
a. The perturbation is
H (t) = q E(t) r = eE0
2
z.
t2 + 2
b. Dipole transition requires that the matrix elements
n l m H (t) nlm = eE0
2
n l m |z | nlm
t2 + 2
are non-zero.
Final Exam - Quantum Mechanics II (40454)
(Dated: May 4, 2009)
INSTRUCTIONS: Write your NAME on the front of the blue exam booklet and sign it.
The exam is open book; you may use your textbook, notes, homework and solution handouts, tables of integrals, e
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