So when I saw Hannah, at the theatre on Saturday night, I could only mime my
impotence and say glancingly, while Horst Eikel loudly joked with Norberte
Uhl, Friday next . . . At first I felt strangely numbed (And the Woods Sing For
Ever was about a clan o
estranged son, a physicistfive times, twice with Malcolm and JB, and once with Harold and
Julia, who were in town for the weekend, and each time he managed to forget that it was his old
friend, his roommate, onstage, and at curtain call, he had felt both
Then, in December, Chip invited her family to his familys Christmas partyan overture that felt like a sneak attack, in
that the invitation, addressed to , came in the mail while she was still finishing exams upstate, and she didnt have a chance
to stop he
Chem MOA
1. (25 points, Harmonic oscillator and first order perturbation theory) The motion of
a particle of mass / is described by the Hamiltonian
H = H, + Hxcfw_x)
with theunperturbed Hamiltonian being thatof the Harmonic Oscillator:
h1 dl
k ,
sh is
ar
Chem 11OA
Name
Spring 2015
KS-^
T. Hayashi
Student ID
TA Name
Midterm Exam I - April 24,2015
Chemistry 110A
Tomoyuki Hayashi, Ph.D.
Instructions: You may use only a pencil or pen. No other materials are allowed.
Write all answers on the exam in the spaces
1a.)
=0
sh is
ar stu
ed d
vi y re
aC s
o
ou urc
rs e
eH w
er as
o.
co
m
= | = 1
= | = 1
= | = 0
=
= (
= (
)(
=0
)
+ ) + ( )( ) ( ) = 0
=
(
+ ) 4( )( ) ( ) )
2
+ ) (
,
= | =
+
6
+
6
Th
= | =
=
= |
=
Chem 110A
Homework 6: Due Friday, May 15, 2015
Chemistry 110A
1. Find the values of the following commutators for the hydrogen atom Hamiltonian.
Only a little algebra is required, because you may use the values of the angular
momentum commutators without
CHE$110A$
HW#$5$
$
1.$
h ( m1 + m2 )
h
h
B=
=
=
2
2
2
8 I 8 r
8 2 r 2 m1m2
$
kg m 2
1.996 10 26 kg + 2.657 10 26 kg )
(
s
=
= 5.78 1010 Hz
2
2
10
26
26
8 (1.1283 10 m ) 1.996 10 kg 2.657 10 kg
6.626 10 34
$
2
sh is
ar stu
ed d
vi y re
aC s
o
ou urc
rs e
e
1.)
(4
4
+ ) = [12
6( ) = 12( )
1 = 2( )
+6
]=0
= 2
= 2
4
= [(12)(13)( )
]
(6)(7)
sh is
ar stu
ed d
vi y re
aC s
o
ou urc
rs e
eH w
er as
o.
co
m
=
= 2
=
4 156
42
4 156 (2)(42)
72
=
=
2
2
2
2
2a.) < >
| | =
( )
= ( )
)
=
= ( )
)( )( )
1
1
The following wave function (in which A and B are numbers not functions of x or
E1 t
E1 t
t) (x, t) = A1 (x)e ~ + B2 (x)e ~ is a linear combination of two solutions of the time
En t
dependent Schr
odinger equation each having the form n (x)e ~ with n=1
Chapter 8. Quantum theory: introduction and principles
8.4.3 The information in a wavefunction
c) Superpositions and expectation values:
The Schrdinger equation for a particle of mass m free to move parallel to the x-axis
with zero potential energy is:
Th
Chem 110A
Homework 6: Due Friday, May 15, 2015
Chemistry 110A
1. Find the values of the following commutators for the hydrogen atom Hamiltonian.
Only a little algebra is required, because you may use the values of the angular
momentum commutators without
Chem 110A
Homework 8: Due Wednesday, June 3 2015
Chemistry 110A 2015
Tomoyuki Hayashi, Ph.D.
These problems cover material in both chapter 8 and chapter 9 of McQuarrie and
Simon. Additional review problems are also suggested here
1. Properties of a Slater
1
The following wave function (in which A and B are numbers not functions of x or
E1 t
E1 t
t) (x, t) = A1 (x)e
+ B2 (x)e
is a linear combination of two solutions of the time
En t
dependent Schrdinger equation each having the form n (x)e
o
with n=1 and 2,
Chem 110A
Homework 7, Due Monday, May. 22, 2015
Chemistry 110A - 2015
Tomoyuki Hayashi, Ph.D.
1. Algebraic solution of a two term linear variational approximation
problem (2 x 2 eigenvalue problem). (Not a Mathematica or MatLab
problem, but you can use th
CHEM 110A
Tentative Syllabus posted in week I
Chemistry 110A
Instructor:
Quantum Mechanics
Tomoyuki Hayashi, Ph.D.
T. Hayashi
Spring 2015
[email protected]
Prerequisites: Taking this course without having completed the prerequisite mathematics
and phy
CHE 110A
HW# 5
1.
h ( m1 + m2 )
h
h
B=
=
=
2
2
2
8 I 8 r
8 2 r 2 m1m2
kg m 2
(1.996 1026 kg + 2.657 1026 kg )
s
=
= 5.78 1010 Hz
2
2
10
26
26
8 (1.1283 10 m ) 1.996 10 kg 2.657 10 kg
6.626 10 34
for Joules use E = h B
1-7 Sirius, one of the hottest known stars, has approximately a blackbody spectrum
with Jim = Eﬁﬂnm. Estimate the surface temperature of Sirius.
[3525069573 1r“ J sjlﬁsswgnssx 103 lung's} H .1 59.3.5553 “3—: m K
SDlutiDE A=:rmi'inar =5 T=rn§im3m~ "
T 3 2-