* rgmih (4.] ad m
' A+B> GD ._ 91g 4. Y2_' '
WAB _=§(_CD) Mm 711; a, 1; 1
04% 3km Wm" '_ol§5= COM] +D (4:1) (5].
u I ' -' 'tch
' QM, (QT-t? CH: CemL+De°tL: Fe
. ' 1. m
' (4wqu Ema em .C=.- L13?
. mm M?» La 1. "2A"
Problem Set 5, PHYS 271
1. A 100 W beam of light is shone onto and completely absorbed by a
blackbody of mass m=2x10-3 kg for 104s. The blackbody is initially at rest in
a frictionless space.
(a) Compute the total energy and momentum absorbed by the black
Problem Set 6, PHYS 271
1. Consider the interstellar propulsion system described in the Nature paper
by Professor G. Marx. But in a modified scheme replace the mirror attached
to the space vehicle by the black body absorber. As you remember from the
simil
Problem Set 10, PHYS 271
1. Find an expectation value <x> for a simple harmonic oscillator in a
nonstationary state described by the wave function
E t
E t
i 1
i 2
1
(x,t) =
+ u 2 (x)e ,
u1 (x)e
2
1
2
where E n = + n .
2. Apply the uncertainty princi
Phys 271 Winter 2012 Assignment 5
1. [4 marks] Harris 4.58
[Note: In class we discussed a pure Gaussian wave function e x / 2 x for simplicity.
Here they are discussing the more general case we alluded to consisting of the product of
a Gaussian envelope a
Phys 271 Winter 2011 Assignment 6 Solutions
1. Starting with a particle in the nth energy eigenstate of the infinite square well
described by the wavefunction:
n ( x) 2 / L sin(n x / L)
(a) compute x n , x 2 n , p n , p 2 n .
(b) compute the product of t
Phys 271 Winter 2011 Assignment 7 Solutions
Chapter 6 Questions
1. (SMM 7.12)
A potential model of interest for its mathematical simplicity is the delta well. The delta
well may be thought of as a square well of width L and depth S/L in the limit L0.
The
Problem Set 11, PHYS 271
1. A stream of quantum particles of mass m and energy E is incident on a
potential barrier of length L (0<x<L) and heights V0, where E<V0. Show
using a direct approach, i.e. by employing smoothness conditions, that the
transmissio
Problem Set 4, PHYS 271
1. Two identical masses m are initially at rest, a distance L apart. A constant
force F accelerates one of them toward the other until they collide and stick
together. What is the (rest) mass of the resulting particle?
2. The Higgs
Phys 271 Winter 2012 Assignment 7
1. [6] The Delta Well (See Harris 5.47 and 6.26 for further discussion) - Scattering
States and the Bound State
A potential model of interest for its mathematical simplicity is the delta well. The delta
well may be though
Problem Set 3, PHYS 271
1. The radar speed trap operates on a frequency 0=109 Hz. What is the beat
frequency between the transmitted signal and one received after reflection
from a car moving at v=30 m/s toward the radar. Do calculations with
accuracy to
Phys 271 Winter 2012 Assignment 7 Solutions
1. [6] The Delta Well (See Harris 5.47 and 6.26 for further discussion) - Scattering
States and the Bound State
A potential model of interest for its mathematical simplicity is the delta well. The delta
well may
Problem Set 8, PHYS 271
1. How are the stationary-state solutions, u(r), of the Schrdinger equation
changed if a constant is added to the potential V(r)? Show that this change
has no consequences on the probability density and expectation values. (This
me
Problem Set 9, PHYS 271
1. Consider the one-dimensional problem of a particle of mass m in a
potential
V = , x < 0
V = 0, 0 x L
V = V0 , x > L
(a) Show that the bound state energies (E<V0) are given by the equation
tan
2mEL
E
=
V0 E
(b) Without solving an
Problem Set 7, PHYS 271
1. Consider an experiment in which a beam of electrons is directed at a plate
containing two slits, labeled A and B. Beyond the plate is a screen equipped
with an array of detectors which enables one to determine where the
electron
Summary 13
q Blackbody radiation in a hohlraum, whose walls are
maintained at some temperature T. The vessel is filled by
radiation in thermodynamical
equilibrium that is emitted by
the walls. Probability density
of the modes at energy En and
temperature
Summary 1
Law of inertia: a force free body remains at rest or in a
state of rectilinear and uniform motion in the inertial frame.
Inertial frames are not unique.
Galilei transformation between two inertial reference
systems: x=x+vt, y=y, z=z
ux=ux+v, u
Summary 10
q Relativistic mass From momentum conservation (by
postulating invariance of the transverse momentum py=py)
m(u) =
m0
#u&
1 % (
$c'
q Linear momentum
q Second Newtons law
2
= (u)m0
!
!
p = m0 (u)u
!
! ! !
! dp
!
3 (u a) u
F= =m 0 (u)a+m 0 (u)
d