Physics V2600 Quantum Mechanics II
Lecture: Tuesday and Thursday 10:00 – 11:50 AM Room J/410
Office: MR311C, Office hours: Tuesday 1:00-1:50 PM, Wednesday 11:00-11:50 AM
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 http://portal.cuny.edu
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
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
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
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
Wigner-Weisskopf line shape
Fano-Anderson line shape
Welton’s treatment of Lamb shift
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
The Virial Theorem
Einstein-Podolsky Rosen paradox
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.
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:
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: http://www1.ccny.cuny.edu/CCNYBulletin/upload/2007_09_UGraduateBulletin…).
Joel I. Gersten
Academic Integrity and Plagiarism
The CUNY Policy on Academic Integrity can be found at
This policy defines cheating as “the unauthorized use or attempted use of material, information, notes, study aids, devices or communication during an academic exercise.” The CUNY Policy on plagiarism says the following about plagiarism (the CUNY Policy can be found in Appendix B.3 of the CCNY Undergraduate Bulletin 2007 -2009 as well as the web site listed above):
Plagiarism is the act of presenting another person’s ideas, research or writings as your own. The following are some examples of plagiarism, but by no means is it an exhaustive list:
1. Copying another person’s actual words without the use of quotation marks and footnotes attributing the words to their source.
2. Presenting another person’s ideas or theories in your own words without acknowledging the source.
3. Using information that is not common knowledge without acknowledging the source.
4. Failing to acknowledge collaborators on homework and laboratory assignments.
5. Internet plagiarism includes submitting downloaded term papers or parts of term papers, paraphrasing or copying information from the internet without citing the source, and “cutting and pasting” from various sources without proper attribution.
The City College Faculty Senate has approved a procedure for addressing violations of academic integrity, which can also be found in Appendix B.3 of the CCNY Undergraduate Bulletin.”