Solutions to Problems in Goldstein, Classical Mechanics, Second Edition
Homer Reid December 1, 2001
Chapter 3
Problem 3.1
A particle of mass m is constrained to move under gravity without friction on the inside of a paraboloid of revolution whose axis is
4130 HOMEWORK 6 Due Thursday April 1
(1) Let A R. A point x A is called isolated if it is not a cluster point of A. (a) Can an open set have an isolated point? Can a closed set have one? (b) Give an example of a countable set with no isolated points. (2)
4130 HOMEWORK 5 Due Tuesday March 9 (1) A subset I of R is called an interval if for all x, y I and all z R, if x < z < y then z I . Show that if I is a bounded interval, then (inf I, sup I ) I . Using this, show that I must be one of the following four i
MATH 413 FINAL EXAM Math 413 nal exam, 13 May 2008. The exam starts at 9:00 am and you have 150 minutes. No textbooks or calculators may be used during the exam. This exam is printed on both sides of the paper. Good luck! (1) (20 marks) Let X = (0, 1] R.
MATH 413 FINAL EXAM Math 413 nal exam, 13 May 2008. The exam starts at 9:00 am and you have 150 minutes. No textbooks or calculators may be used during the exam. This exam is printed on both sides of the paper. Good luck! (1) (20 marks) Let X = (0, 1] R.
Physics 3316, Spring 2010 Basics of Quantum Mechanics Study Guide for Prelim 1
This study guide contains a brief outline of the material covered in class thus far. The initial discussion in class focused on various experimental discoveries that pointed to
PHYS 3316 Solutions: Problem Set 4
1 Propagation of wavepackets in an external potential
(a) The motion of a particle in a potential U (x) is described by the Hamiltonian H= p2 + U (x) . 2m (1)
The force acting on this particle due to the potential is F =
Quantum States and Operators Physics 3316 - Basics of Quantum Mechanics Spring 2010
Quantum States
The rst step in building a theory capable of predicting the results of experiments carried out on a physical system is to develop a description of the diere
Physics 3316, Spring 2010 Basics of Quantum Mechanics Problem Set 6
(Due in lecture, March 10, 2010)
Required Readings : French and Taylor Ch. 4, Griths Ch. 2 Key concepts: Solutions to the time independent Schrdinger equation, Manipulation of operators o
Physics 3316, Spring 2010 Basics of Quantum Mechanics Problem Set 5
(Due in lecture, March 03, 2010)
Required Readings : Key concepts: Manipulation of quantum operators, Properties of quantum operators (Linearity, Hermitian operators), Time dependent Schr
Physics 3316, Spring 2010 Basics of Quantum Mechanics Problem Set 4
(Due in lecture, Feb 22, 2010)
Required Readings : French and Taylor Ch. 3, Griths Ch. 1
1
Propagation of wavepackets in an external potential
In lecture, we considered the correspondence
4130 HOMEWORK 3 Due Thursday February 18
(1) Let cfw_xn and cfw_yn be Cauchy sequences of rational numbers. Prove that cfw_xn cfw_yn if and only if for all > 0 there exists N N such that for all m, n > N , |xm yn | < . Let () be the condition: for all
Physics 3318, Spring 2013
Assignment 7
l. H&F 6.2
2. H&F 6.6
3. H&F 6.8
4. H&F 6.10
5. H&F 6.14
6. Consider the most general point transformation for one degree of freedom, Q =
Q(q, t). Show that the form of the Euler-Lagrange equation is unchange
Poisson distributions and counting statistics
Mukund Vengalattore
Introduction
This note contains a brief description of the properties of a Poisson distribution. This process describes the statistics of a wide range of random, independent events that occ
PHYS 3316 Solutions: Problem Set 5
1 Angular Momentum Operator
Consider a wavefunction = () for (, ], such that ( ) = ( ) , and consider an operator L = i . (1) (2)
(Henceforth, we will often use the notation used in lectures to denote the inner product O
Week 1 notes
Sunday, January 24, 2010 6:48 PM
New Section 1 Page 1
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New Section 1 Page 5
. end with example of measurement of momentum of a mixed state. Next week . time dependent to TISE . beg
MIDTERM EXAM, PHYSICS 5306, Fall, 2002 Dr. Charles W. Myles Take Home Exam: Distributed, Wednesday, October 23 DUE, IN MY OFFICE OR MAILBOX, 5PM, MON., OCT. 28. NO EXCEPTIONS! TAKE HOME EXAM RULE: You are allowed to use almost any resources (books from th
Physics 318: First prelim exam
Thursday, February 22, 2007 Duration: 90 minutes Instructions: Answer all questions. This is a closed book exam. There are 15 points for Q1, 15 for Q2 and 10 for Q3.
1. A pendulum which is exposed to gravity consists o
Solutions to Homework #4
February 18, 2008
1
a.) The time needed to travel between (x1 , y1 ) and (x2 , y2 ) along y(x) is given by T [y] =
T 0 x2 x1
dt =
dx
dt = dx
x2 x1
dx
ds dt . dx ds
(1)
Here s is the distance along the curve, given by
Physics 318: Solutions to Homework #3
February 18, 2008
1
E = - - A B=A 1 L(x, x, t) = mx2 - q(x, t) + q x A(x, t) 2 (1)
a.) Writing out all the components explicitly, the Lagrangian is given by L(x, y, z, x, y, z, t) = We compute m 2 (x +