Assignment 2
1 Question 1
(x) =
1/4 x2 /2 e . Before proceeding lets check that this is normalized correctly since well need that integral later on anyway. Consider some integral of the form I=
+
Were given
dxeax
2
where a is real and positive. The fun
QUANTUM MECHANICS
PHYSICS 446A Mid-term Exam October 20, 2008 Instructions: Answer all four questions. Closed book exam. Calculators are not permitted. This exam comprises 3 pages. Time allotted is 2 hours. Write down as much information as possible to cl
Assignment #9 (Do not hand-in)
PHYS-446
1. In this problem you will solve the isotropic simple harmonic oscillator problem using the power series method. The potential is
1 2 m r 2 for a particle of mass m . 2
(a) Write the Schrdinger equation for the fun
Assignment #8
PHYS-446
due in class on 28 November 2008
1. (Griffiths, Problem 3.15) Show that two non-commuting operators cannot have a complete set of common eigenfunctions. Hint: Show that if P and Q have a complete set of common eigenfunctions, then [
Assignment #7
PHYS-446
due in class on 21 November 2008
1. Prove Schwarz Inequality: ab a b To do this, consider the axiom cc 0 , applied to
c =a
ba b2
b
2. (Griffiths, Problem 3.27) An operator A , representing observable A , has two normalized eigen
Assignment #6
PHYS-446
due in class on 14 November 2008 1. (Griffiths, problem 3.4) (a) Show that the sum of two hermitian operators is hermitian. (b) suppose Q is hermitian, and is a complex number. Under what condition (on ) is Q hermitian? (c) When is
Assignment #5
PHYS-446
due in class on 7 November 2008 1. (Griffiths, problem 2.21) A free particle has the initial wave function ax x , 0 = A e where A and a are positive real constants. (a) Normalize x , 0 . (b) Find k . (c) Construct x , t , in the for
Assignment #4
PHYS-446
due in c lass on 10 Octob er 2008
1. (Gr iffi ths, pr oblem 2.42) Find t he all owed energ ies of t he hal f harmon ic osc ill ator 1 / 2 m 2 x 2 for x 0 for x 0 (Th is repr esents , for exa mple, a s pring t hat can be stre tched,
Assignment #3
PHYS-446
due in class on 3 October 2008
1. A particle is confined to an infinite square well defined as
V x =
cfw_
V 0 0 x 2a otherwise
where V 0 and a are positive real constants. Calculate the general wave function x , t of a particle stuc
Assignment #2
PHYS-446
due in cla ss on 26 Septe mber 2008
1. A par ticl e in f ree space i s in it ial ly in a wave packet descri bed by
x =
Wha t is the expect ati on value of the mo mentu m?
1 /4
e
x / 2
2
2. (S hankar, Prob lem 4.2.3) Show t hat i
Name:_ ID:_
Assignment #1
PHYS-446
due in cla ss on 19 Septe mber 2008 1. (a ) Calcul ate your de Broglie wavel ength as you walk down Mi lto n str eet. Assum e some reali st ic va lues of t he quant iti es you need. How s mal l (widt h) would a door have