Department of Electrical Engineering

Engineering Quantum Mechanics

EE 539, 4 Units

Fall 2017

9:00 am - 10:50 am, TTH, VHE210

 
Instructor: Tony Levi Office Hours: TTH  8:00 a.m. - 8:45 a. m. or by appointment
Office: KAP  132  
Phone: (213) 740-7318 Course outline:
E-mail: alevi@usc.edu Quantum Mechanics Course Outline (This document and all handouts are in PDF format.)
Teaching Assistant: Amine Abouzaid
E-mail: abouzaid@usc.edu
Office Hours:

meeting Mondays and Fridays at 5.00pm in KAP 132From 5.00pm on Mondays and32

Web sites:

http://alevi.usc.edu
http://classes.usc.edu/term-20173/classes/ee/

http://classes.usc.edu/term-20173/finals/

Grading:      Final Exam:
Midterm 35%      11:00 a.m. - 1:00 p.m.
Homework 10%      Thursday, December 7, 2017
Final Exam  55%      VHE210
     
Required Text: First day of EE539 classes Tuesday, August 22, 2017
Applied Quantum Mechanics Last day of EE539 classes Thursday, November 30, 2017
A.F.J. Levi  

Applied Quantum Mechanics, A.F.J. Levi, Cambridge University Press, Paperback: Call Cambridge University Press at (845) 353-7500 and ask for the "Print on demand version" ISBN: 978-0-521-18399-4

Optional Texts: Essential Classical Mechanics for Device Physics, IoP, ISBN: 9781681744124

Optimal Device Design, Cambridge University Press, ISBN: 0521116600

   
Problems and example exams Papers: 
MATLAB code Quantum fluctuations in small lasers
     Roy-Choudhury 2011
  Negative refractive index resonators
     Schmidt 2007
  Opto-mechanical resonators
     Vahala 2007
  Single electron memory
       Huang 2004
       Yano Review 1999
    Single electron transistor
       Uchida 2003
    Tunnel FET
       Saraswat 2008
    Quantum communication
       Bennett 1992
       Bienfang 2004
       Gisin Review 2002

 

Abstract
Quantum mechanics is the basis for understanding physical phenomena on the atomic and nano-meter scale.  There are numerous applications of quantum mechanics in biology, chemistry and engineering.  Those with significant economic impact include semiconductor transistors, lasers, quantum optics and photonics.  As technology advances, an increasing number of new electronic and opto-electronic devices will operate in ways that can only be understood using quantum mechanics.  Over the next twenty years fundamentally quantum devices such as single-electron memory cells and photonic signal processing systems will become common-place.  The purpose of this course is to cover a few selected applications and to provide a solid foundation in the tools and methods of quantum mechanics.  The intent is that this understanding will enable insight and contributions to future, as yet unknown, applications.

Prerequisites
Mathematics:
A basic working knowledge of differential calculus, linear algebra, statistics, and geometry.
Computer skills:
An ability to program numerical algorithms in C, MATLAB, FORTRAN or similar language and display results in graphical form.
Physics background:
Should include a basic understanding of Newtonian mechanics, waves, and Maxwell's equations.


Introduction:  Lectures 1 - 5

 

Lecture 1-2

REVIEW OF CLASSICAL CONCEPTS

Extended discussion to include material from the book “Essential classical mechanics for device physics”.

The linear and nonlinear oscillator

                        Electromagnetism

                        Mechanical model of light-matter interaction due to Lorentz.

 

Lecture 3        

TOWARDS QUANTUM MECHANICS – PARTICLES AND WAVES

                        Diffraction, interference, and correlation functions for light

                        Black-body radiation and evidence for quantization of light

                        Photoelectric effect

THE PHOTON PARTICLE

The existence of the photon particle

The photon at a beam splitter

                        Secure quantum communication

 

Lecture 4-5        

WAVE-PARTICLE DUALITY

The link between quantization of photons and quantization of other particles

                        Diffraction and interference of electrons

                        When is a particle a wave?

THE SCHRDINGER WAVE EQUATION

                        The wave function description of an electron of mass m0 in free-space

                        The electron wave packet and dispersion

The Bohr model of the hydrogen atom

                                    Calculation of the average radius of an electron orbit in hydrogen

                                    Calculation of energy difference between electron orbits in hydrogen

                        Periodic table of elements

                        Crystal structure

                                    Three types of solid classified according to atomic arrangement

                                    Two-dimensional square lattice, cubic lattices in three-dimensions

                        Electronic properties of semiconductor crystals

The semiconductor heterostructure

 

 

Using the Schrdinger wave equation:  Lectures 6 - 7

Lecture 6-7

            INTRODUCTION

            The effect of discontinuities in the wave function and its derivative

WAVE FUNCTION NORMALIZATION AND COMPLETENESS

INVERSION SYMMETRY IN THE POTENTIAL

                        Particle in a one-dimensional square potential well with infinite barrier energy

            NUMERICAL SOLUTION OF THE SCHRDINGER EQUATION

                        Matrix solution to the descretized Schrdinger equation

Nontransmitting boundary conditions. Periodic boundary conditions

CURRENT FLOW

                        Current flow in a one-dimensional infinite square potential well

                        Current flow due to a traveling wave

DEGENERACY IS A CONSEQUENCE OF SYMMETRY

                        Bound states in three-dimensions and degeneracy of eigenvalues

BOUND STATES OF A SYMMETRIC SQUARE POTENTIAL WELL

                        Symmetric square potential well with finite barrier energy

TRANSMISSION AND REFLECTION OF UNBOUND STATES

                        Scattering from a potential step when effective electron mass changes

                        Probability current density for scattering at a step

                        Impedance matching for unity transmission

PARTICLE TUNNELING

            Electron tunneling limit to reduction in size of CMOS transistors

THE NONEQUILIBRIUM ELECTRON TRANSISTOR

 

 

Scattering in one-dimension:  The propagation method:  Lectures 8 - 10

Lecture 8

THE PROPAGATION MATRIX METHOD

            Writing a computer program for the propagation method

TIME REVERSAL SYMMETRY

CURRENT CONSERVATION AND THE PROPAGATION MATRIX

 

Lecture 9

THE RECTANGULAR POTENTIAL BARRIER

                        Tunneling

RESONANT TUNNELING

                        Heterostructure bipolar transistor with resonant tunnel barrier

Localization threshold

                        Multiple potential barriers

THE POTENIAL BARRIER IN THE d-FUNCTION LIMIT

ENERGY BANDS IN PERIODIC POTENTIALS:  THE KRONIG-PENNY POTENTIAL

                        Bloch’s theorem

                        Propagation matrix in a periodic potential

                        Real and imaginary band structure

 

Lecture 10

            THE TIGHT BINDING MODEL FOR ELECTRONIC BAND STRUCTURE

                        Nearest neighbor and long-range interactions

                        Crystal momentum and effective electron mass

USE OF THE PROPAGATION MATRIX TO SOLVE OTHER PROBLEMS IN ENGINEERING

THE WKB APPROXIMATION

                        Tunneling

 

 

Related mathematics:  Lecture 11 - 12

Lecture 11-12

ONE PARTICLE WAVE FUNCTION SPACE

PROPERTIES OF LINEAR OPERATORS

            Hermitian operators

            Commutator algebra

DIRAC NOTATION

MEASUREMENT OF REAL NUMBERS

            Time dependence of expectation values. Indeterminacy in expectation value

            The generalized indeterminacy relation

THE NO CLONING THEOREM

DENSITY OF STATES

            Density of states of particle mass m in 3D, 2D, 1D and 0D

Quantum conductance

Numerically evaluating density of states from a dispersion relation

Density of photon states

 

 

The harmonic oscillator:  Lectures 13 - 14

Lecture 13

THE HARMONIC OSCILLATOR POTENTIAL

CREATION AND ANNIHILATION OPERATORS

                        The ground state. Excited states

            HARMONIC OSCILLATOR WAVE FUNCTIONS

                        Classical turning point

            TIME DEPENDENCE

                        The superposition operator. Measurement of a superposition state

 

Lecture 14

                        Time dependence in the Heisenberg representation

                        Charged particle in harmonic potential subject to constant electric field

            ELECTROMAGNETIC FIELDS

                        Laser light     

                        Quantization of an electrical resonator

Quantization of lattice vibrations

                        Quantization of mechanical vibrations

 

 

Review:  Lecture 15

 

 

Midterm:

 

 

Fermions and Bosons:  Lecture 17 - 19

Lecture 17

INTRODUCTION

The symmetry of indistinguishable particles. Slater determinant

Pauli exclusion principle. Fermion creation and annihilation operators – application to tight-binding Hamiltonian

FERMI-DIRAC DISTRIBUTION FUNCTION

Equilibrium statistics

Writing a computer program to calculate the chemical potential and Fermi-Dirac distribution at finite temperature

BOSE-EINSTIEN DISTRIBUTION FUNCTION
CURRENT AS FUNCTION OF VOLTAGE BIAS

Semiconductor heterostructure diode structures in the depletion approximation.

Metal-insulator-metal.

Reduced dimensions

 

Lecture 18 - 19     

PHOTON FOCK STATES

                        The Mandel effect

                        n-photons at a beam splitter

                        n-photons at a FP resonator

            THE MANDEL EFFECT

                        Dual photon source

                        Fiber-optic beam splitter and delay line

                        Photon counting and correlation

 

 

Time dependent perturbation theory and the laser diode:  Lectures 20 - 22

Lecture 20

FIRST-ORDER TIME-DEPENDENT PERTURBATION THEORY

                        Abrupt change in potential

                        Time dependent change in potential

            CHARGED PARTICLE IN A HARMONIC POTENTIAL

            FIRST-ORDER TIME-DEPENDENT PERTURBATION

FERMI’S GOLDEN RULE

IONIZED IMPURITY ELASTIC SCATTERING RATE IN GaAs

                        The coulomb potential. Linear screening of the coulomb potential

Correlation effects in position of dopant atoms

                        Calculating the electron mean free path

 

Lecture 21

EMISSION OF PHOTONS DUE TO TRANSITIONS BETWEEN ELECTRONIC STATES

                        Density of optical modes in three dimensions

                        Light intensity

                        Background photon energy density at thermal equilibrium

                        Fermi’s golden rule for stimulated optical transitions

                        The Einstein A and B coefficients

                        Occupation factor for photons in thermal equilibrium in a two-level system

                        Derivation of the relationship between spontaneous emission rate and gain

THE SEMICONDUCTOR LASER DIODE

Spontaneous and stimulated emission. Optical gain in a semiconductor. Optical gain in the presence of electron scattering

DESIGNING A LASER CAVITY

Resonant optical cavity.  Mirror loss and photon lifetime

The Fabry-Perot laser diode. Rate equation models

 

 

Lecture 22

            NUMERICAL METHOD OF SOLVING RATE EQUATIONS

The Runge-Kutta method. Large-signal transient response. Cavity formation

NOISE IN LASER DIODE LIGHT EMISSION

                        Effect of photon and electron number quantization

Langevin and semiclassical master equations

QUANTUM THEORY OF LASER OPERATION

Density matrix

Single and multiple quantum dot, saturable absorber

 

 

Time independent perturbation theory:  Lectures 23

Lecture 23

NON-DEGENERATE CASE

Hamiltonian subject to perturbation W

First-order correction.  Second order correction

Harmonic oscillator subject to perturbing potential in x, x2 and x3

DEGENERATE CASE

Secular equation

Two states

Perturbation of two-dimensional harmonic oscillator

Perturbation of two-dimensional potential with infinite barrier

 

 

Angular momentum, the hydrogenic atom, and bonds:  Lectures 24 - 25

Lecture 24

ANGULAR MOMENTUM

Classical angular momentum

The angular momentum operator

Eigenvalues of the angular momentum operators Lz and L2

Geometric representation

             SPHERICAL HARMONICS AND THE HYDROGEN ATOM

                        Spherical coordinates and spherical harmonics

The rigid rotator

Quantization of the hydrogenic atom

Radial and angular probability density

 

Lecture 25

ELECTROMAGNETIC RADIATION

No eigenstate radiation

Superposition of eigenstates

Hydrogenic selection rules for dipole radiation

Fine structure

BONDS.

The hydrogen molecule ion.

The hydrogen molecule covalent bond

Valence bond description.

Molecular orbital description

The ionic bond

 

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