MASSACHUSETTS INSTITUTE OF TECHNOLOGY Spring 2006 Assignment #1 Due Thursday, February 16 at 4pm Physics 8.04 Vuletic page 1 of 2
Note that the derivation or formula, and not just the end result, is always required. 1. Photon energy scale I. (25 points) A
A. Selected formulae Time-dependent Schroedinger equation:
Time-independent Schroedinger equation:
i
( x, t ) H ( x, t ) t
H ( x ) E ( x )
Position representation of Hamiltonian operator
Position representation of momentum operator
Momentum representati
y y y y y
T#5#T# ~ |y uY8jjy
# # #G
tj # | x R 5 Wy
~ #x5m$x#Y5#5x 5 z ucfw_y 5x5u5445!f#x #$5#I#xgY#5I#xlYjoy ~ ~ ~ |y cfw_ y #'uj v j r | rtyj ' v y u x z | | 1 | 5#5t5rt # y I Rm xT ~ | y ~ ~ uY'm18cfw_$5x5u5 5#5t#x ~ ~ ~ ~ y 5YI5v!25$j#Cg5uY8c
A. Physical constants and conversion factors Quantity Atomic mass unit Electron mass Proton mass Elementary charge Planck !"#$%#$ Symbol amu Value 931.5 1.661 10-27 me 0.511 9.109 10-31 mp 939 1.673 10-27 q 1.602 10-19 h 6.626 10-34 4.136 10-15 -34 =h/2 1
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics Physics 8.04 EXAM 2 Tuesday, March 14, 2006 11:00am-12:30pm Spring 2006
FAMILY (Last) NAME
GIVEN (First) NAME
Student ID Number
Instructions: 1. SHOW ALL WORK. All work must be done in the exam b
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics Physics 8.04 EXAM 1 Tuesday, March 14, 2006 11:00am-12:30pm Spring 2006
FAMILY (Last) NAME
GIVEN (First) NAME
Student ID Number
Instructions: 1. SHOW ALL WORK. All work must be done in the exam b
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Spring 2006 Optional assignment #11 Physics 8.04 Vuletic page 1 of 1
Suggested reading for assignment #11: G8-1 to 8-3, F&T 12-1 to 12-6
1. Hydrogen atom
Assume that nlm denotes an eigenfunction of the hydrogen atom w
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Spring 2006 Assignment #10 Due Thursday, May 11 at 4pm Physics 8.04 page 1 of 2 Vuletic
Let 0 be the normalized ground state of the harmonic oscillator, defined by a 0 0 and
1. Operators and the HO (30 points)
0 0 1
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Spring 2006 Assignment #9 Due Thursday, May 4 at 4pm Physics 8.04 page 1 of 3 Vuletic
1. Transmission probability for a potential barrier and a potential well. (20 points) a) In lecture 16 we derived that the transmis
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Spring 2006 Assignment #8 Due Thursday, April 20 at 4pm Physics 8.04 page 1 of 2 Vuletic
1. Qualitative bound state solutions I (20 points).
French & Taylor, Problem 3-15.
(a) Draw the wave functions associated with
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Spring 2006 Assignment #7 Due Thursday, April 13 at 4pm Physics 8.04 page 1 of 3 Vuletic
1. Gaussian wavepacket in free space. (30 points). A free particle of mass m has the initial wave function
( x , t 0)
2
1
w1/
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Spring 2006 Assignment #6 Due Thursday, April 6 at 4pm Physics 8.04 page 1 of 2 Vuletic
1. Time evolution of wavefunction in box potential (40 points). Consider a particle of mass m inside a box of size a with infinit
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Spring 2006 Assignment #5 Due Thursday, March 23 at 4pm Physics 8.04 page 1 of 2 Vuletic
1. Continuity equation for probability density and probability current (20 points) A particle is in a state described by a wavef
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Spring 2006 Assignment #4 Due Thursday, March 9 at 4pm Physics 8.04 Vuletic page 1 of 2
1. Time delay in photoelectric effect. (15 points) A beam of ultraviolet light (=121 nm) of intensity 10nW/cm2 and area A=1cm2 i
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Spring 2006 Assignment #3 Due Thursday, March 2 at 4pm Physics 8.04 Vuletic page 1 of 3
1. Compton effect and electron recoil. (25 points) a) Show that it is impossible for a free electron to absorb all of the energy
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Spring 2006 Assignment #2 Due Thursday, February 23 at 4pm
1.
Physics 8.04
Vuletic page 1 of 2
Parsevals theorem. (10 points)
Prove the following theorem: A function (x) and its Fourier transform (k) have the same nor
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