Physics 157 Introductory Physics for Engineers
Thermal physics and Waves
Dr. Andrzej Kotlicki [email protected]
Learning goals.

Describe a physical situation with a mathematical model.
Identify the appropriate physical concepts that describe a sit
Reading 1 Week of September 5
The reading material for this week is from Chapter 17 found in
Sections: 17.1, 17.2, 17.3, 17.4
When reading you shouldn't read every detail. The point is to
concentrate on the Important Terminology. In addition, study the li
Chapter 19: The First Law of Thermodynamics
Thermodynamic System: Any collection of objects that is convenient to regard as a unit and
that may have the potential to exchange energy with its surroundings

Thermodynamic process: changes in thermodynamic s
Physics 157
University of British Columbia
Kaili Sun
Chapter 20: The Second Law of Thermodynamics

It is impossible for any system to underfo a process in which it absorbs heat from a reservoir at a
single temperature and converts the heat completely int
Chapter 39.5 Continuous Spectra
Emission line spectra come from matter in the gaseous state.

A heated solid or liquid emits radiation with a continuous distribution of wavelengths.
Most ideal surface for emitting light with continuous spectrum is one th
University of British Columbia
Physics 157 Notes
Kaili Sun
Chapter 11.411.5
11.4: Stress, Strain, and Elastic Moduli
Deformable body: any body of any object that can be changed


Applying stress (measure of forces causing a deformation) to a changeably
Phys 500, Quantum Mechanics
Homework 4
O
* The ClebschGordan Issue *
Posted: Friday, November 7; due: Monday, November 17
Problem 1: The Heisenberg spin chain and SU(2)symmetry. (5 points)
Remark 1: In this problem, we go back to the Heisenberg spin c
Phys 500, Quantum Mechanics
Reference Solution for Homework 3
November 9, 2014
Problem 1. (3 points) Demonstrate the following three properties of density operators, starting
from their definition (where all states in the ensemble are normalized to unity)
Phys 500, Quantum Mechanics
Reference solution for Homework 1
Posted: Friday, September 26, 2014
Problem 1 (5 points): In class we introduced the Hermitian adjoint X of an operator X through the dual
correspondence
Xi hX , i H.
(1)
Denote by [X] the ma
Phys 500, Quantum Mechanics
Homework 5 Reference Solution
Solution to Problem 1. Because H must be Hermitian, V12 is real. Energies up to second order
perturbation are given by
En =
En(0)
+ hn
(0)
V n
(0)
2
i+
X hk (0) V n(0) i2
k6=n
so
(0)
E1 = E1 +
Tsymmetry
In theoretical physics, Tsymmetry is the theoretical symmetry of physical laws under a time reversal
transformation:
T : t 7 t.
Although in restricted contexts one may nd this symmetry, the observable universe itself does not show
symmetry und
Phys 500, Quantum Mechanics
Homework 3
Posted: Tue, Oct 16, 2012 Due: Mon, Oct 22, 2012, 1PM.
Problem 1: Quantum states and tensor product Hilbert spaces. (5 points) How
many physically relevant real parameters are required to specify the state vector of
Mixed, pure, and entangled quantum states.
Density matrix
Quantum Information and Quantum Optics course, 2013
Goran Johansson, Thilo Bauch, Jonas Bylander
Chalmers, MC2
September 24, 2013
The density operator or density matrix is a more general way of des
Phys 500, Quantum Mechanics
Homework 1
Posted: Wed, September 17, 2014 Due: Fri, September 26, 2014, 1PM.
Problem 1 (5 points): In class we introduced the Hermitian adjoint X of an operator X
through the dual correspondence
Xi hX , i H.
(1)
Denote by [
Phys 500, Quantum Mechanics
Homework 2
Posted: Wed, October 1, 2014 Due: Fri, October 10, 2014, 1PM.
Problem 1 (5 points). Show that the Gaussian wave packet i with
x2
2 1/4
(x) := hxi = (2d )
exp 2
4d
p
p
saturates the Heisenberg uncertainty relation,
Lecture notes for Phys 500 QM I
*
Fall term 2013
From: Robert Raussendorf, November 30, 2013.
Abstract. These lecture notes cover material which is not in Sakurais book. We discuss probabilistic mixtures of quantum states, density operators and their prop
Phys 500, Quantum Mechanics
Reference solution for Homework 2
Posted: October 12, 2014
Problem 1 (5 points). Show that the Gaussian wave packet i with
x2
(1)
(x) := hxi = (2d2 )1/4 exp 2
4d
p
p
saturates the Heisenberg uncertainty relation, i.e., h(x)2
Phys 500, Quantum Mechanics
Homework 5
Posted: Fri, Nov 21, 2014 Due: Fri, Nov 28, 2014, 1PM.
Problem 1: Timeindependent perturbation theory. (5 points) Consider the Hamiltonian H = H0 + V of a twostate system
!
(0)
E1
0
0 V12
Ho =
, V =
,
(0)
V12 0
0 E
Phys 500, Quantum Mechanics
Reference solution for Homework 1
Posted: Wednesday, September 25, 2013
Problem 1 (5 points): In class we introduced the Hermitian adjoint X of an operator X through the dual
correspondence
Xi ! hX , 8 i 2 H.
(1)
Denote by [
8. WKB Approximation
The WKB approximation, named after
Wentzel, Kramers, and Brillouin, is a method
for obtaining an approximate solution to a
timeindependent onedimensional differential
equation, in this case the Schr
odinger
equation. Its principal a
Phys 500, Quantum Mechanics
Homework 4 Reference Solution
November 25, 2012
Solution to Problem 1: (a). First, Sz
=
[H, Sz ] =
n 1
g~3 X
8
i=1
=
=
"
n 1
g~3 X h
8
i=1
n 1
g~3 X
8
= 0.
(i) (i+1)
x x
~
2
+
Pn
k=1
(k)
z .
(i) (i+1)
y
y
Thus,
+
(i) (i+1)
,
z
Kramers theorem
1 See also
In quantum mechanics, the Kramers degeneracy theorem states that for every energy eigenstate of a timereversal symmetric system with halfinteger total spin,
there is at least one more eigenstate with the same energy. In other w
Phys 500, Quantum Mechanics
Reference Solution for Homework 3
November 6, 2013
Problem 1 (5 points): Consider a particle subject to a onedimensional simple harmonic oscillator
potential. Suppose at t = 0 the state vector is given by
!
aP
exp
i
0i,
~
fo
Phys 500, Quantum Mechanics
Reference Solution for Homework 3
October 24, 2012
Problem 1: Quantum states and tensor product Hilbert spaces. (5 points) How
many physically relevant real parameters are required to specify the state vector of n spin
1/2 part
Lecture notes for Phys 500 QM I
*
2014
From: Robert Raussendorf, October 8, 2014.
Abstract. These lecture notes cover material which is not in Sakurais book. We discuss probabilistic mixtures of quantum states, density operators and their properties, tens
Phys 500, Quantum Mechanics
Homework 5 Reference Solution
November 26, 2012
The problems are appended for reference.
Solution to Problem 1: If the barrier is of infinite height, every energy level is twofold degenerate. For finite barrier height, all deg
Phys 500, Quantum Mechanics
Homework 5 Reference Solution
The problems are appended for reference.
Solution to Problem 1: If the barrier is of infinite height, every energy level is twofold degenerate. For finite barrier height, all degeneracies are lift
Phys 500, Quantum Mechanics
Reference solution for Homework 2
Posted: Tuesday, October 16, 2012
Problem 1 (5 points). By considering position eigenkets xi, with Xxi
= xxi, show that the
momentum operator P is the generator of translations, i.e.,
i
exp