Chapter 3 Quantum statistics
Each photon then interferes only with itself. Interference between two dierent photons never occurs. Paul Dirac, The Principles of Quantum Mechanics, Fourth Edition, Chapter 1 Note 1: Quantum interference is interference betwe
PHY2822 Exp.5 Prelab ex Balmer series of H Electron transition: from n = 4 to n = 2. Wavelength = 486.1 nm Energy E = h =
hc
=
1240 eV nm = 2.551 eV 486.1 nm
Ch.1
PHYS 2041 Problems in Quantitative Methods for Basic Physics (1st Term 10/11)
Chapter 1
Elementary Numbers
Functions
and
Complex
1.1 Exponential and Logarithmic Functions
The exponential function of x is denoted as e x or exp x and the inverse functi
PHYS2004 (1st Term 10/11)
Assignment 1
Section A (Compulsory due on 22/09/2010 Wed (before 5:00 pm ) 1.
(a) Given that a i k and b 3i 2 4k , find (i) the projection vector of j j a in the direction of b , and (ii) the projection vector of b in the direct
PHYS2004 (1st Term 10/11)
Assignment 2
Section A (Compulsory due on 30/09/2010 Thu (before 5:00 pm) 1. Show that the four points: A 1, 1, 0 , B 2, 0, 1 , C 2, 1, 2 and D 4, 4, 1 coplanar and find the equation of the plane containing them. [50 marks] 2. Fi
PHYS2004 (1st Term 10/11)
Assignment 3
Section A (Compulsory due on 14/10/2010 Thu (before 5:00 pm) 1. A point P moves on the curve
r a exp cot ,
in such a way that its radius vector OP rotates about the origin with the constant
angular velocity . Find t
PHYS2004 (1st Term 10/11)
Assignment 4
Section A (Compulsory due on 21/10/2010 Thu (before 5:00 pm) 1.
The curvature of a curve traced out by the position vector r t is defined as
dr d 2 r 2 dt dt 3 . dr dt
Find , given that (a) (b) r t a sin ti a cos t
Ch.2
PHYS2041 Problems in Quantitative Methods for Basic Physics (1st Term 10/11)
Chapter 2
Differential and Integration
2.1 Concepts of Limit and Continuity
2.1.1 Definition of Limit:
A function F, which is defined on the domain x1 x c and c x x2 ,
is sa
Ch.3
PHYS2041 Problems in Quantitative Methods for Basic Physics (1st Term 10/11)
Chapter 3
Techniques of Integration
3.1 Method of Substitution
One may make the integration of a function simpler by using substitution of variable. To illustrate the method
Ch.1
PHYS2004 Quantitative Methods for Basic Physics I (1st Term 10/11)
Chapter 1
Vector Algebra, Coordinate Systems and Related Topics
1.1 Vector Algebra
1.1.1 Scalars and Vectors
Scalars: quantities require only a real number to represent their size (or
PHYS 5510: Advanced Statistical Physics
Ren-Bao Liu Department of Physics, The Chinese University of Hong Kong [email protected] 2010-2011, 1st Term c Copyright reserved. No reproduction or redistribution of any part is allowed without written permission
Electricity and Magnetism
Overview
All matters possess a property called charge, interactions between charges give rise to almost all the phenomena we experienced in our daily life (except for the effects from gravity). Anything you can think of, e.g. co
Ch.2
PHYS2004 Quantitative Methods for Basic Physics I (1st Term 10/11)
Chapter 2
Some Applications of Calculus
2.1 Maxima and Minima of Functions
2.1.1 Stationary Points
A point at which the derivative of a function f x vanishes,
f x0 0 .
(2.1.1)
A stati
Chapter 2 Review of statistical mechanics
13
14
CHAPTER 2. REVIEW OF STATISTICAL MECHANICS
2.1 Principles of statistical mechanics
2.1.1 Macroscopic and microscopic states
A macroscopic system is made of a huge number of particles. The power of thermodyna
Ch.3
PHYS2004 Quantitative Methods for Basic Physics I (1st Term 10/11)
Chapter 3
Ordinary Differential Equations
An ordinary differential equation is an equation containing ordinary (not partial) derivatives of the unknown function. The order of an ordin
Boundary values problems in electrostatics
The uniqueness theorem If we specified the potentials at all the boundaries (i.e. surfaces) of a charge-free region of space, and want to know the potentials at every points in the region, we have a boundary valu
PHY2822 Exp. 4 Prelab ex. 2:
R R B ( x ) =k [ R 2 + ( x ) 2 ]3/ 2 + [ R 2 + ( x + ) 2 ]3/ 2 x 2 2 NIR 2 where k 0 . 2
R R 3( x ) 3( x + ) dB( x ) 2 2 =k + R R dx [ R 2 + ( x ) 2 ]5 / 2 [ R 2 + ( x + ) 2 ]5 / 2 2 2
R 2 5/ 2 R2 2 R 2 3/ 2 2 [ R + ( x 2 ) ]
Maximally ecient quantum thermal machines: The basic principles
Sandu Popescu
H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom (Dated: September 15, 2010) Following the result by Skrzypczyk et al., ar
THE CHINESE UNIVERSITY OF HONG KONG Department of Physics Second Term, 2009-2010 PHY 0222 Physics Problems II
Date Topic Group Time Room
REVISED 8.01.10
Jan 13
Jan 20
Jan 27
Feb 3
Feb 10
Feb 24
Mar 3
Mar 10
Mar 17
Mar 24
Mar 31
Apr 7
A B C D E F G H I J K
Electrostatic field in dielectric media
All matters consist of charged constituents (i.e. electrons and nuclei) that can be displaced by an electric field. For e.g. : an electric dipole could be formed by applying an E-field on an originally symmetrical
Ch.4
PHYS2004 Quantitative Methods for Basic Physics I (1st Term 10/11)
Chapter 4
Functions of Two or More Variables
4.1 Partial Derivatives
4.1.1 Introduction
If y f x ,
dy dx
= the slope of the curve y f x ; OR = the rate of change of y with respect to
Chapter 4 Non-ideal gases
In this chapter we consider gases of short-range interaction. The short-range is dened by that the integration of the potential between two particles over the space converges, i.e., the potential decays faster than r3 for r being
Magnetostatics
Introduction We wish to introduce the magnetic field from a different perspective. Suppose the only knowledge we have are electrostatics and special relativity, and we never heard of magnetic force before. Using a simple argument, we will s
Ch.5
PHYS2004 Quantitative Methods for Basic Physics I (1st Term 10/11)
Chapter 5
Transcendental Functions
5.1 Transcendental Functions
By definition, y f x is an algebraic function of x if it is a function that satisfies an irreducible algebraic equation
Chapter 5 Phase Transition I: van der Waals Gas
5.1 General remarks
Phase transitions occur at discontinuities of the equilibrium thermodynamic functions with varying certain physical parameters such as temperature, density, magnetic eld, etc. For a nite
Magnetic fields in matter
All matters contain magnetic moments, either from the orbital motion of a charge particle (e.g. electron in an atom) or from the intrinsic properties of an elementary particle the spin There are three major kinds of magnetic res
Chapter 6 Phase transition II: Ising model (A)
In this chapter we discuss the phase transition of Ising model, using the mean-eld approximation. The Ising models partition function can be exactly calculated in one- and two-dimensional lattices. It provide
Electrodynamics
In electrostatics and magnetostatics, both the E-field and Bfield are time-independent. They are relevant to cases where we have a fixed charge distribution and steady current Faraday discovered that a changing magnetic flux through a cir
Chapter 7 Phase Transition III: Landau Theory
7.1 Order parameter
In Landau theory of phase transition, a phase transition is signaled by the emergence of a thermodynamic quantity, which is zero above the transition temperature and grows (or jumps) to be