1
Show that the particle-in-a-box wave functions, which are given by, n (x) =
! nx "
2
L
s
L
sin L , n = 1, 2, satisfy the relation, 0 n (x) m (x) = 0 for m = n where here the
complex conjugate is ir
Show that the particle-in-a-box wave functions, which are given by, n (x) =
1
L
sin
, n = 1, 2, satisfy the relation, 0 n (x) m (x) = 0 for m = n where here the
complex conjugate is irrelevant since
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 3
Chem 110A
Homework 5: Due Friday, May 8, 2015
Chemistry 110A 2015
Tomoyuki Hayashi, Ph.D.
Problems 2 and 3 on this homework set involve the same concepts as problems 6-10 and
6-13 in the text.
1. Rigi
Chem 110A Homework 5: Due Friday, October 30, 2009 Chemistry 110A 2009 Professor McCurdy Problems 2 and 3 on this homework set involve the same concepts as problems 6-11 and 6-13 to 6-15 in the text.
The theme I have for this problem solution set is getting used to picking out the salient features of
a solutions so that you can generalize and reuse the work you do.
To this end, Dirac notation is p
Name SOLUTI O N
Answer any four of the following five questions. Please circle the numbers of the
problems that you want us to grade. Otherwise, we will just grade the first four
problems. You must sh
Chem 110A
Homework 7: Due Friday, May 13, 2016
Chemistry 110A
Professor McCurdy
1. Mathematica/MatLab Problem: Variational calculation on the hydrogen atom
using a linear combination of Gaussian basis
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
Chem 110A
Homework 5: Due Friday, May 8, 2015
Chemistry 110A 2015
Tomoyuki Hayashi, Ph.D.
Problems 2 and 3 on this homework set involve the same concepts as problems 6-10 and
6-13 in the text.
1. Rigi
Chem 110A
Homework 6: Due Friday, November 14, 2014
Chemistry 110A
Professor McCurdy
1. Find the values of the following commutators for the hydrogen atom Hamiltonian.
Only very little algebra is requ
CHEMISTRY 110A
Final Exam
Monday December 10th 2012
Name_
A, B = AB BA
x
sin 2x
d
du
(sin u) = (cos u )
dx
dx
2
sin xdx = 2 4
x 2 x sin 2x cos 2x
x sin xdx = 4 4 8 2
d
du
(cos u ) = (sin u)
dx
dx
Homework Week 3: Due Friday, October 16 Chemistry 110A 2009 Professor McCurdy 1. Problem 4-25 in McQuarrie and Simon The algebra should be very short and its a good idea to do this one before problem
Homework Week 2: Due Friday, October 17
Chemistry 110A 2014
Professor McCurdy
1. Properties of wave functions. Show by explicit integration that the particle-in-a-box
wave functions, which are given b
Homework Week 3: Due Friday, October 24
Chemistry 110A 2014
Professor McCurdy
1. [This problem can be done either using Dirac notation or not. ] The following
wave function (in which A and B are numbe
Chem 110A Homework Week 4: Due Friday, October 23 Chemistry 110A 2009 Professor McCurdy 1. Make the harmonic approximation to each of the following diatomic potential energy functions to obtain the co
Homework Week 2: Due Friday, October 9 Chemistry 110A 2009 Professor McCurdy 1. Problem 3-16 in McQuarrie. 2. (a) Find the average value of position x , momentum p , and square of the mometum p 2 for
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 pro
1a
Using atomic units, for the quantities in the general formula for the energy
Z2
e2
levels of a one electron atom, En = 2n2 a0 4 0 , show that the energy of the helium ion
(He+ , with Z = 2) in its
1a
x2 dx
xe
Show that
Solution:
is 0.
=0
The integrand is an odd function, and it is integrated over symmetric limits, so the answer
Beyond that, to evaluate over arbritary limits, let u = x2 = du =
1-7 Sirius, one of the hottest known stars, has approximately a blackbody spectrum
with Jim = lnm. E-stirnate the surface temperature of Sirius.
. mammary: 10- J 5 2.9979241: 103 me . - -5
50mm: A =
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 a
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 be
Homework Week 2: Due Tuesday, July 11
Chemistry 110A 2017
Tomoyuki Hayashi, Ph.D.
1. Properties of particle-in-a-box eigenstates
(a) Find the average value of position x , momentum p , and square of t