Engineering Quantum Mechanics
Instructor:  Tony Levi  Office Hours: TTH 8:00 a.m.  8:45 a. m. or by appointment 
Office:  KAP 132  
Phone:  (213) 7407318  Course outline: 
Email:  alevi@usc.edu  Quantum Mechanics Course Outline (This document and all handouts are in PDF format.) 
Teaching Assistant:  Amine Abouzaid  
Email:  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 

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) 3537500 and ask for the "Print on demand version" ISBN: 9780521183994 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  
RoyChoudhury 2011  
Negative refractive index resonators  
Schmidt 2007  
Optomechanical 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 nanometer 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
optoelectronic devices will operate in ways that can only be understood using
quantum mechanics. Over the next twenty years fundamentally quantum devices
such as singleelectron memory cells and photonic signal processing systems will
become commonplace. 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 12
Extended discussion to include material from the book “Essential classical mechanics for device physics”.
The linear and nonlinear oscillator
Electromagnetism
Mechanical model of lightmatter interaction due to Lorentz.
Lecture 3
Diffraction, interference, and correlation functions for light
Blackbody 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 45
WAVEPARTICLE DUALITY
The link between quantization of photons and quantization of other particles
Diffraction and interference of electrons
When is a particle a wave?
The wave function description of an electron of mass m_{0} in freespace
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
Twodimensional square lattice, cubic lattices in threedimensions
Electronic properties of semiconductor crystals
The semiconductor heterostructure
Using the Schrödinger wave equation: Lectures 6  7
Lecture 67
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 onedimensional square potential well with infinite barrier energy
NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION
Matrix solution to the descretized Schrödinger equation
Nontransmitting boundary conditions. Periodic boundary conditions
Current flow in a onedimensional infinite square potential well
Current flow due to a traveling wave
Bound states in threedimensions and degeneracy of eigenvalues
BOUND STATES OF A SYMMETRIC SQUARE POTENTIAL WELL
Symmetric square potential well with finite barrier energy
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 onedimension: 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
Tunneling
Localization threshold
Multiple potential barriers
THE POTENIAL BARRIER IN THE dFUNCTION LIMIT
Bloch’s theorem
Propagation matrix in a periodic potential
Real and imaginary band structure
Lecture 10
Nearest neighbor and longrange interactions
Crystal momentum and effective electron mass
USE OF THE PROPAGATION MATRIX TO SOLVE OTHER PROBLEMS IN ENGINEERING
Tunneling
Lecture 1112
ONE PARTICLE WAVE FUNCTION SPACE
PROPERTIES OF LINEAR OPERATORS
Hermitian operators
Commutator algebra
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
Lecture 13
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
The symmetry of indistinguishable particles. Slater determinant
Pauli exclusion principle. Fermion creation and annihilation operators – application to tightbinding Hamiltonian
Equilibrium statistics
Writing a computer program to calculate the chemical potential and FermiDirac distribution at finite temperature
Semiconductor heterostructure diode structures in the depletion approximation.
Metalinsulatormetal.
Reduced dimensions
Lecture 18  19
The Mandel effect
nphotons at a beam splitter
nphotons at a FP resonator
THE MANDEL EFFECT
Dual photon source
Fiberoptic beam splitter and delay line
Photon counting and correlation
Time dependent perturbation theory and the laser diode: Lectures 20  22
Lecture 20
Abrupt change in potential
Time dependent change in potential
CHARGED PARTICLE IN A HARMONIC POTENTIAL
FIRSTORDER TIMEDEPENDENT PERTURBATION
FERMI’S GOLDEN RULE
The coulomb potential. Linear screening of the coulomb potential
Correlation effects in position of dopant atoms
Calculating the electron mean free path
Lecture 21
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 twolevel system
Derivation of the relationship between spontaneous emission rate and gain
Spontaneous and stimulated emission. Optical gain in a semiconductor. Optical gain in the presence of electron scattering
Resonant optical cavity. Mirror loss and photon lifetime
The FabryPerot laser diode. Rate equation models
Lecture 22
NUMERICAL METHOD OF SOLVING RATE EQUATIONS
The RungeKutta method. Largesignal transient response. Cavity formation
Effect of photon and electron number quantization
Langevin and semiclassical master equations
Density matrix
Single and multiple quantum dot, saturable absorber
Time independent perturbation theory: Lectures 23
Lecture 23
Hamiltonian subject to perturbation W
Firstorder correction. Second order correction
Harmonic oscillator subject to perturbing potential in x, x^{2} and x^{3}
Secular equation
Two states
Perturbation of twodimensional harmonic oscillator
Perturbation of twodimensional potential with infinite barrier
Angular momentum, the hydrogenic atom, and bonds: Lectures 24  25
Lecture 24
Classical angular momentum
The angular momentum operator
Eigenvalues of the angular momentum operators L_{z} and L^{2}
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
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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