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Physics 115A, Problem Set 4
Due Tuesday, October 20 @ 5pm in the box outside Broida 1019 (PSR)
Suggested reading: Griffiths 2.3
1
Constructing States
Given the explicit solution for the ground state of the harmonic oscillator,
0 (x) =
m 1/4
~
m
e 2~ x
2
Physics 115A, Problem Set 3
Due Tuesday, October 13 @ 5pm in the box outside Broida 1019 (PSR)
Suggested reading: Griffiths 2.1-2.3
1
E and V for normalizable solutions
Griffiths Problem 2.2:
Show that E must exceed the minimum value of V (x), for every n
Physics 115A, Problem Set 6
Due Tuesday, November 3 @ 5pm in the box outside Broida 1019 (PSR)
Suggested reading: Griffiths Section 2.5, 2.6
1
SHO in Momentum Space
= p2 + 1 m 2 x
The harmonic oscillator Hamiltonian in any representation is H
2 . So lets
Physics 115A, Problem Set 5
Due Tuesday, October 27 @ 5pm in the box outside Broida 1019 (PSR)
Suggested reading: Griffiths 2.4. Study for the midterm!
1
The 3D Harmonic Oscillator
Next quarter, when we encounter quantum systems in three spatial dimension
Physics 115A, Problem Set 7
Due Tuesday, November 10 @ 5pm in the box outside Broida 1019 (PSR)
Suggested reading: Griffiths Section 2.6, 3.1. If you have not studied linear algebra
recently, please read the Appendix in Griffiths carefully.
1
From the Squ
Physics 115A, Problem Set 9
Due Tuesday, November 24 @ 5pm in the box outside Broida 1019 (PSR)
Suggested reading: Griffiths Section 3.4-3.6.
1
Proof that 0 = 1?
=
Consider a Hermitian operator A with some eigenvector |ai with real eigenvalue a, A|ai
a|a
Physics 115A, Solution Set 2
1
Macroscopic Wavelengths
The idea that matter has a wave-like nature pertains not just to particles, but to macroscopic objects as well. Its just typically the case that the relevant wavelength is far too
small to detect; its
Physics 115A, Solution Set 3
1
E and V for normalizable solutions
Griffiths Problem 2.2:
Show that E must exceed the minimum value of V (x), for every normalizable solution to
the time-independent Schr
odinger equation. What is the classical analog to thi
Physics 115A, Problem Set 2
Due Tuesday, October 6 @ 5pm in the box outside Broida 1019 (PSR)
Suggested reading: Griffiths 1.5-1.6, 2.1
1
Macroscopic Wavelengths
The idea that matter has a wave-like nature pertains not just to particles, but to macroscopi
Physics 115A, Problem Set 8
Due Tuesday, November 17 @ 5pm in the box outside Broida 1019 (PSR)
Suggested reading: Griffiths Section 3.1-3.4.
1
Hilbert Space
1. Show that the set of all square-integrable functions (that is, the set of functions f (x)
Rb
f
PHYS 115A Homework 4 Solutions Winter 2008
revisions added February 12: see ADDITIONAL NOTE below and Problem 1
The message below was emailed to the class before this homework assignment was due: As noted at the beginning of class, the lecture notes
1
University of California, Santa Barbara Department of Physics Physics 115A - Midterm - Winter 2006 A.N. Cleland
Closed notes, closed book; you are allowed one sheet of formulas and a calculator.
Some identities that you might nd useful:
eu d
PHYS 115A Midterm Solutions Winter 2008
Problem 1
Recall that the normalized energy eigenstates and energies for an innite well of width a extending from x = a/2 to x = +a/2 are: E n = n2 n (x) = n (x) = 2 2 2ma2 2 nx cos a a 2 nx sin a a for odd n =
Physics 115A, Problem Set 1
Due Tuesday, September 29 @ 5pm in the box outside Broida 1019 (PSR)
Suggested reading: Griffiths 1.1-1.5
1
Discrete statistics at the Tour de France
Related to Griffiths section 1.3.1
Suppose were lucky enough to gather all 61
Physics 115A, Solution Set 1
NC
1
Discrete statistics at the Tour de France
Related to Griffiths section 1.3.1
Suppose were lucky enough to gather all 61 winners of the Tour de France in one
room, alive and dead (greetings, zombie Jacques Anquetil!). One
Midterm exam Part II. Please work all 3 problems. Dont worry if you cant finish, but *do*
move on to!the next part if you get stuck.!
!
1. (28 pts) A particle of mass m is confined in an infinite square well of width L:
V = 0 for 0 x L; and V = , otherwis
Practice Midterm problems
Please work using the posted cover sheet, which contains the information you will be provided
for the actual midterm. (If needed, additional integrals will be provided with the problem, as in
problem 2 below).
For these practice
Physics 115A, Solutions to Problem Set 8
1
Hilbert Space
1. Show that the set of all square-integrable functions (that is, the set of functions f (x)
Rb
for which a |f (x)|2 dx is finite on a specified interval x [a, b]) is a vector space.
Rb
2. Show that
Practice Midterm, Physics 115A
This practice midterm contains problems in the spirit of those you will encounter on
the actual midterm. The length of the practice exam has not been carefully calibrated to
match the actual midterm, so dont worry if this ta
Physics 115A, Solution Set 6
1
SHO in Momentum Space
= p2 + 1 m 2 x
The harmonic oscillator Hamiltonian in any representation is H
2 . So lets
2m
2
consider the simple harmonic oscillator in momentum space, where we define the position
and momentum opera
1. Probability Densities:
Dirk goes to work by driving through stop-and-go trac every day for 1 hour.
60
Thus, his velocity can be modeled as v(x) = 1+5 sin(x)2 where x is given in miles and
v(x) is given in miles/hr.
(a) Use separation of variables to sh
PHYS 115A: Quantum Mechanics
UCSB Fall quarter 2014
Professor Dirk Bouwmeester
Problem Set 3
This problem set is due on Wednesday October 22, at 5:00PM. Please turn in your answers
in the box outside the Physics Study Room (Broida 1019).
Problem 1: Schrdi
Jimmy Shen
PHYS 115A
Homework #4
October 29, 2014
2.38
(a)
In the new well of width 2a the allowed energies and wave functions are:
q
2 2 2
2
En = n p h 2 ;
yn ( x ) = 2a sin np x
2a
2m(2a)
The wavefunction at t = 0 is:
(q
2
p
for x < a
a sin a x
Y (x) =
Practice Midterm, Physics 115A
This practice midterm contains problems in the spirit of those you will encounter on
the actual midterm. The length of the practice exam has not been carefully calibrated to
match the actual midterm, so dont worry if this ta
Physics 115A, Problem Set 5
Due Tuesday, October 27 @ 5pm in the box outside Broida 1019 (PSR)
Suggested reading: Griffiths 2.4. Study for the midterm!
1
The 3D Harmonic Oscillator
Next quarter, when we encounter quantum systems in three spatial dimension
Practice Final Exam, Physics 115A
Fall 2015
This exam is closed book, closed notes, closed calculators/phones. Please show your work
for full credit. You may make free use of anything on the Useful Formulae page.
This practice exam contains problems in th
Physics 115A, Solutions to Problem Set 9
1
Proof that 0 = 1?
=
Consider a Hermitian operator A with some eigenvector |ai with real eigenvalue a, A|ai
a|ai. Suppose |ai is normalizable and properly normalized, ha|ai = 1. Consider a second
and suppose tha
Phys 219
Midterm Exam
02/12/15
Instructions: Show all work. Write clearly. Number all pages turned in and number
responses by question and part. Make sure your exam has five sides printed (six
questions on two sides and three sides of information). Good l