Lecture 1.
Electric Charge and Electric Field
ZHANG Baile
School of Physical and Mathematical Sciences,
Nanyang Technological University
1
2
Vocabulary Test
A neutral object
A. Is identical to an
insulator.
B. Has no charge of either
sign.
C. Has no net

Mathema'cal framework I
Hilbert space
State vector and wavefunc5on
Dirac nota5on
Operators
Matrix representa5on
Func5on of operators
Commutator algebra
Hilbert space
Linear vector space V
Elements:
vectors:
scalars:
, , ,

Angular Momentum II
General angular momentum
Raising, lowering operators
Matrix representation
Spin angular momentum
Spin one-half
1
General angular momentum: J2 and Jz
To account for intrinsic magnetic moment of elementary particles, eg. electrons.

Postulates of QM II
Time evolution of a state; stationary states
Time evolution of operators and expectation values
Measurement and uncertainty principle
Symmetries and Conservation laws
Time evolu2on
Postulate 5: The time evolution of a QM syst

PH3101 QUANTUM MECHANICS II
Week 3: TIME EVOLUTION AND SYMMETRIES AND CONSERVATION LAWS
Symmetries and Conservation Laws
Prof Pinaki Sengupta
College of Science
School of Physical and Mathematical Sciences
Content Copyright Nanyang Technological Universit

PH3101 QUANTUM MECHANICS II
Week 3: TIME EVOLUTION AND SYMMETRIES AND CONSERVATION LAWS
Time Evolution of a Quantum Mechanic System II
Prof Pinaki Sengupta
College of Science
School of Physical and Mathematical Sciences
Content Copyright Nanyang Technolog

PH3101 QUANTUM MECHANICS II
Week 3: TIME EVOLUTION AND SYMMETRIES AND CONSERVATION LAWS
Time Evolution of a Quantum Mechanic System
Prof Pinaki Sengupta
College of Science
School of Physical and Mathematical Sciences
Content Copyright Nanyang Technologica

PH3101 QUANTUM MECHANICS II
Week 3: TIME EVOLUTION AND SYMMETRIES AND CONSERVATION LAWS
Conservation of Probability
Prof Pinaki Sengupta
College of Science
School of Physical and Mathematical Sciences
Content Copyright Nanyang Technological University
1
C

PH3101 QUANTUM MECHANICS II
Week 3: TIME EVOLUTION AND SYMMETRIES AND CONSERVATION LAWS
Generalised Uncertainty Principle
Prof Pinaki Sengupta
College of Science
School of Physical and Mathematical Sciences
Content Copyright Nanyang Technological Universi

PH3101 QUANTUM MECHANICS II
Week 3: TIME EVOLUTION AND SYMMETRIES AND CONSERVATION LAWS
Symmetries and Conservation Laws II
Prof Pinaki Sengupta
College of Science
School of Physical and Mathematical Sciences
Content Copyright Nanyang Technological Univer

PH3101 QUANTUM MECHANICS II
Week 3: TIME EVOLUTION AND SYMMETRIES AND CONSERVATION LAWS
Time Evolution and Expectation Value
Prof Pinaki Sengupta
College of Science
School of Physical and Mathematical Sciences
Content Copyright Nanyang Technological Unive

Angular Momentum I
Orbital Angular Momentum L
Eigenvalues and eigenfunctions of L2 and Lz
Particle on a sphere and rigid rotator
General angular momentum : J2 and Jz
1
Orbital Angular Momentum
Describes particle moving in a closed orbit.
Angular momen

Postulates of QM
State vector / wavefunction
Observable / operator
Measurement
State of a system
Postulate 1: Every quantum mechanical system is described by a complexvalued wave function or state vector which contains all the information about

1
2
PH3101 / PAP 311
Quantum Mechanics II
Introduc)on
&
General Administra)on
Pinaki Sengupta
SPMS-PAP-05-03
6592-1801
[email protected]
3
Schedule
LESS
ON
DAY
TIME
LOCATION
TUE
10.30 - 12.30 SPMS-LT3
FRI
11.30 -

Chapter 4, Semiconductor Science & Light emitting Diodes
4.1 Semiconductor concept & energy bands
A. Formation of energy band
The energy of the bound electron of the
hydrogen atom is quantized.
When two H atoms are brought close,
their electron wavefuncti

Chapter 2 Dielectric Waveguides and Optical Fibers
Prof. Charles Kao is awarded Noble prize in Physics on 6 Oct. 2009.
The part of 2009's award associated with Mr. Kao underscores the fact that optical fibers carry an
increasing fraction of phone calls, t

Chapter 7: Photovoltaic Devices
Energy: A Big Issue
It is predicted that the world annual energy consumption will grow from the
current 13 terawattyear (1012 Wyr or TWyr) to as much as 30 TWyr by
2050. Currently most of the energy is produced by burning n

Since the discovery of lasers in 1960, some 15 physics
Nobel prizes have been awarded for achievements
directly related or linked to lasers.
1
Only four years after the laser was
invented, the film Goldfinger (1964)
featured a memorable scene that had
eve

Application of Polarization
1
2
3
LCD Optics
Basic Structure of a LCD
ITO: Indium Tin Oxide
is transparent and conductive.
*
*
*
*
*
*
4
Basic Operating Principle
LCD
operates
by
polarization manipulation
of light using electrical
pulses.
Polarization c

2.6 Bit-rate, dispersion, and optical bandwidth
In digital communications, signals are generally sent as light pulses along an
optical fiber. Information is first converted to an electrical signal in the form of
pulses that represent bits of information.

Chapter 6: Photodetectors
Photodetector: devices that convert a light signal to an electrical signal
such as a voltage or current.
Critical thinking question: what specifications do we concern for a photodetector?
Photodetector classification: Thermal Det

Chapter 3: Polarization and Modulation of Light
3.1 Polarization
A. State of polarization
A propagating EM wave has its electric and magnetic field perpendicular to the
direction of propagation. The term polarization describes the behavior of the
electric

4.4 The pn-junction band diagram-no bias
1
4.4 The pn-junction band diagram-forward bias
2
4.4 The pn-junction band diagram-reverse bias
3
4.5 Light Emitting Diodes (LEDs)
A. Principles
When a voltage is applied across a pn junction, electrons and holes a

Single frequency semiconductor lasers
1. Frequency-selective dielectric mirrors
There are several methods to ensure a single mode of radiation in the semiconductor
laser cavity. One is to use frequency-selective dielectric mirrors at the cleaved surfaces

Mathema'cal framework II
Commutator algebra
Eigenvalue and eigenvector
Eigenvalue problem in matrix language
Change of basis and unitary transforma9on
Posi9on and momentum space representa9ons
Commutator algebra
Action of

Tutorial 11 solutions
Self-practice questions
1.
2.
.
Questions to be discussed during tutorial
1.
(a)
I Sav
2
Emax
P
0cP
, Emax
2
20c 4 r
2 r 2
P 60 0.05 W 3 W
Emax
Bmax
(b)
(4 107 m/A)(3 108 m/s)(3 W)
2 0.3 m
2
45 V/m
Emax
45 V/m
1.5 107 T
8
c
(3