Syllabus Spring 2018 Physics V2600 General Syllabus


Physics V2600            Quantum Mechanics II        

Course code  

Textbook:        Modern Quantum Mechanics, Revised Edition, J. J. Sakurai, Addison-Wesley, Reading, 1994.


Principles of Quantum Mechanics, Second Edition, R. Shankar, Kluwer Academic/Plenum Publishers, New York, 1994.

Quantum Mechanics, E. Merzbacher, Third Edition, Wiley, New York, 1998.

Quantum Mechanics, Third Edition, L. I. Schiff, McGraw-Hill, New York, 1968.

Quantum Mechanics (two volumes), A. Messiah, Dover, 1999.

Quantum Mechanics, L. D. Landau and E. M. Lifschitz, Addison-Wesley, Reading MA, 1958.

Quantum Mechanics (two volumes), C. Cohen-Tanoudji, B. Diu and F. Laloe, Wiley, New York, 1977.

Introduction to Quantum Mechanics, Second Edition, D. J. Griffiths, Pearson Prentice Hall, Upper Saddle River NJ, 2005.

Introduction to Quantum Mechanics, H. J. W. Muller-Kirsten, World Scientific

Lectures on Quantum Mechanics, G. Baym, Addison-Wesley, 1990.


Grading: Midterm (40%), Final (40%), Homework (20%).

Homework is to be assigned and is due one week after being assigned.


Blackboard website: through CUNY Portal at


Preliminary syllabus


Lecture 1                     a)         Time-independent perturbation theory

b)         Applications of time-independent perturbation theory

c)         Zeeman effect and spin-orbit interaciton


Lecture 2                     a)         Zeeman effect and spin-orbit interaction – Part 2

b)         The two level system

c)         The hyperfine interaction in hydrogen



Lecture 3                     a)         Identical particles and statistics

b)         Bound-state perturbation theory applications, continued:

                                                            Electric polarizability in perturbation theory

                                                            Electric polarizability of hydrogen atom                                                                                            Ground state of the Helium atom

                                                            Van der Waals interaction

                                    c)         Bose-Einstein and Fermi-Dirac statistics


Lecture 4                     a)         Degenerate perturbation theory

                                                            Two-level systems

                                                            Higher number of levels

                                    b)         Inhomogenous linear equations (D’Algarno and Lewis)

                                                            Electric polarizability via inhomogeneous equation

c)         Hellman-Feynman theorem

d)         The no-crossing rule

e)         No permanent electric dipole moments

                                    f)         Kramers degeneracy


Lecture 5                    a)          The WKB approximation
                                   b)          Validity criterion
                                   c)          Connection formulae

                                                            Via Bessel functions to interpolate

                                                            Via asymptotic behavior in complex plane
                                   d)         Bound states


Lecture 6                    a)          Central forces and Langer modification
                                   b)          Normalization of WKB wave-functions
                                   c)          Cold emission from metals
                                   d)         Gamow factor
                                   e)          Time dependent perturbation theory
                                   f)          Adiabatic approximation
                                   g)          Sudden approximation


Lecture 7                    a)          Formal perturbation theory
                                   b)          Dyson chronological product
                                   c)          Stopping of charged particles in matter


Lecture 8                    a)          Harmonic perturbations

                                   b)          Fermi Golden Rule
                                   c)          Density of states and phase space
                                   d)         Phototonization of hydrogen atom
                                   e)          Born and Fock approximation
                                   f)          Fermi theory of beta decay


Lecture 9                    a)          Self-induced transparency
                                   b)          Green’s functions, retarded and advanced
                                   c)          Free particle Green’s function
                                   d)         Integral equation for G
                                   e)          Differential equation for G


Lecture 20                  a)          Feynman diagram interpretation
                                   b)          Scattering matrix
                                   c)          Unitarity of S-Matrix
                                   d)         Symmetry of S-Matrix
                                   e)           T-matrix
                                   f)          Generalized Fermi Golden Rule
                                   g)          Energy representation


Lecture 11                  a)          Lippmann-Schwinger equation
                                   b)          Energy resolved free Green’s Function
                                   c)          Scattering amplitude
                                   d)         Asymptotic behavior of a packet
                                   e)          Born approximation
                                   f)          Yukawa potential
                                   g)          Validity criteria for Born approximation
                                   h)          Outgoing states for photoemission
                                   i)           Eikonal approximation


Lecture 12                   a)         Atom-atom scattering for Van der Waals potential

                                    b)         Atom-atom scattering for Lennard Jones potential

                                    a)         Electron atom scattering neglecting exchange

                                    d)         Distorted wave Born approximation

  1. Kramers-Kronig relation for optics


Lecture 13                   a)         Angular momentum representation of the S-Matrix

b)         Born approximation for phase shifts

                                    c)         Analytic properties of the S-matrix

d)         Levinson’s theorem


Lecture 14                   a)         Review of problems in scattering theory

                                    b)         Symmetric and Antisymmetric wave functions

                                    c)         The exclusion principle

                                    d)         Collision of identical particles including spin effects

                                    e)         The Fermi sea


Lecture 15                   a)         Screening of a charge in a solid

                                    b)         Thomas-Fermi Atom

                                    c)         Neutron Stars

                                    d)         Density matrix

                                    e)         Rearrangement collisions



Lecture 16                   a)         Hartree equations

                                    b)         Hartree-Fock equations

                                    c)         Relativistic Schrodinger equation

                                    d)         Dirac equation

e)         Dirac matrices


Lecture 17                   a)         Angular momentum operator

                                    b)         Continuity equation

                                    c)         Velocity and Zitterbewegung

                                    d)         Nonrelativistic reduction of atom in magnetic field

                                    e)         Free particle solution


Lecture 18                   a)         Coulomb solution to Dirac equation

                                    b)         Solution of Dirac electron in plane electromagnetic wave

                                    c)         Lorentz covariance of Dirac equation


Lecture 19                   a)         Explicit form of Spinor Lorentz matrix for rotations and boosts

                                    b)         Negative energy states, positions, pair creations, Klein

                                         paradox, spin-statistics theorem

                                    c)         Charge conjugation

                                    d)         Parity of Dirac spinors

                                    e)         Bilinear covariants

                                    f)         Nonrelativistic reduction of current density


Lecture 20                   a)         Specific neutron-electron interaction

                                    b)         Foldy-Wouthuysen transformation

                                    c)         Neutrino

                                    d)         Relativistic Rutherford scattering


Lecture 22                   a)         Wave equation for a string

                                    b)         Lagrangians for fields

                                    c)         Normal mode expansion

                                    d)         Fock states

                                    e)         Equal time field commutators

                                    f)         Thermal excitation of a string

                                    g)         Quantization of electromagnetic field

                                    h)         Unruh radiation and Rindler coordinates

                                    i)          The spin-statistics theorem


Lecture 22                   a)         Small time decay of a state

  1. Wigner-Weisskopf line shape
  2. Fano-Anderson line shape
  3. Welton’s treatment of Lamb shift
  4. Bethe’s theory of Lamb shift


Lecture 23                   a)         Glauber states

                                    b)         Squeezed states

                                    c)         Lifetime of 2p-state of hydrogen

                                    d)         Einstein A-B argument

                                    e)         A model laser system

                                    f)         Lamb’s theory of the Maser


Lecture 24                   a)         Quantization of elastic field

                                    b)         Quantization of electron field

                             c)         Classical theory of brehmsstrahlung

                             d)         Quantum (NR) theory of brehmsstrahlung

                             e)         Emission from diatomic molecules in rotational transitions

                             f)         The Feynman propagator for electrons


Lecture 25                   a)         The photon propagator

                                    b)         The vertex for electromagnetic coupling

                                    c)         Summary of the Feynman rules

                                    d)         Projection operators

                                    e)         Trace theorems


Lecture 26                   a)         Compton scattering

                                    b)         Pair annihilation


Lecture 27                   a)         The hydrogen molecule ion

                                    b)         The Born-Oppenheimer approximation

                                    c)         The hydrogen molecule

                                                d)         The Berry phase



Lecture 28      

  1. The Virial Theorem
  2. Entanglement
  3. Einstein-Podolsky Rosen paradox
  4. Schrodinger’s cat
  5. Bell’s theorem
  6. No-cloning theorem
  7. Quantum teleportation
  8. GHZ theorem


Class meetings:

       1/27, 1/29, 2/3, 2/5, 2/10, 2/17, 2/19, 2/24, 2/26, 3/3, 3/5, 3/10, 3/12, 3/17, 3/19, 3/24, 3/26, 3/31, 4/2, 4/7, 4/21, 4/23, 4/28, 4/30, 5/5, 5/7, 5/12, 5/14. 


Midterm Examination: 3/17

Final Examination: to be announced:  In range 5/18-5/22.


Course objectives:

After completing Physics V2600 the student should be able to:

1)    understand and apply the use of approximation methods, including: nondegenerate and degenerate time-independent perturbation theory, time-dependent perturbation theory, the WKB approximation, the sudden approximation and the eikonal approximation;

2)    understand and apply the concepts of statistics of identical particles in quantum mechanics;

3)    understand and apply formal scattering theory to quantum systems;

4)    understand and apply the Dirac equation to the dynamics of fermions;

5)    understand an apply elementary field theory concepts to electromagnetic interactions;

6)    understand the role of measurement and quantum reality in quantum mechanics.



Relationship of course to program outcomes:

The outcomes of this course contribute to the following departmental outcome:

  1. Learn laws of physics and solve problems.


Academic integrity:  Academic dishonesty is prohibited in the City Univeristy of New York and is punishable by penalties, including failing grades, and expulsion, as provided in the College Bulletin (see page 312, Appendix B, of The City College Undergraduate Bulletin, 2007-2009:…).


Prepared by

Joel I. Gersten

September, 2008