Howard University
WASHINGTON DC 20059

DEPARTMENT OF PHYSICS AND ASTRONOMY
-- (202) 806-6245 (main office), -5830 (fax)

Quantum Mechanics II
PHYS-221 (CRN: 11684): MW 2:00-3:30 pm in TKH 207;
[Topics][Daily Schedule][Assignments][e-Gear][Welcome]

Instructor: Tristan Hübsch
(Office hours: M 3:30-5:00 pm & T 1:00-5:00 pm & by appointment—please, first check my weekly schedule)
TKH 213, 806-6267 thubsch@mac.com
Textbook and other sources (also @ iTunes U):
required: L.E. Ballentine, Quantum Mechanics recomended: S. Flügge, Practical Quantum Mechanics (try also here)
optional: C. Cohen-Tannoudji, B. Diu & F. Laloe, Quantum Mechanics
optional: E. Merzbacher, Quantum Mechanics (3rd ed.)
optional: D. Bohm, Quantum Mechanics
and several other sources, as given in class and on-line.
Component
Time
Remark
% of Grade
Homework See in daily schedule Late HW = 0 credit !!!
20%
Classwork/Quizzes 2-3/week homework material
20%
Exams (two midterms) See in daily schedule not comprehensive
(each) 20%
Now drop the one worst component above (for each student individually).
Final exam Last week of semester comprehensive
40%

The aim of the course is to give a thorough review of the various applications of quantum mechanics, as introduced in the first part (PHYS-220), and to further develop those and new techniques. To that end, an application of symmetry is further developed, quantum fields statistical mechanics introduced and related to their classical counterparts. In addition, we study concrete applications to (1) Nuclei, (2) Periodic (crystalline) systems, (3) Atomic spectra, (4) Inter-atomic (chemical) forces, (5) Sub-nuclear and “fundamental” physics.

“Success = 1% inspiration + 99% perspiration”--T.A. Edison
But, learning is still 100% learnig + 0% teaching.


Topical schedule:

§12: Time-Dependent Phenomena
§13: Discrete Symmetries
Extra: WKB Approximation and Details of the H-Atom
§14: The Classical Limit
§15: Quantum Mechanics in Phase Space
1st Midterm exam--§12-13+WKB: 02/10 (open text, in-class) + take-home due 02/15 §16: Scattering
Extra: He-Atom, ionized H2-Molecule - Variational Method
§17: Identical Particles
2nd Midterm exam--§14-17+Perturbations and Variations: 03/23 (open text, in-class) + take-home due 03/28
§18: Many Fermions
Extra: Crystals
§19: Quantum Fields
§20: Bell’s Theorem
Final exam--comprehensive: (almost) everything, given 04/13 - due 04/20

Day-to-day schedule: Students are required to read ahead

01/11

Spin dynamics: §12.1
01/13 Exponential and non-exponential decay: §12.2
01/18 Observed Holiday: Martin Luther King, Jr.'s Birthday
01/20 Energy-time indeterminacy and Quantum Beats: §12.3-4 [HW1 due]
01/25 Time-dependent perturbation theory, radiation and adiabatic approximation: §12.5-7
01/27 WKB approximation: extra [HW2 due]
02/01 WKB approximation & alpha-decay: extra
02/03 Discrete symmetries: §13 [HW3 due]
02/08 The classical limit: §14.1-4
02/10 1st Midterm Exam (§12-13 + WKB) open-book + take-home due Monday, 02/15, 5:00 pm
02/15 Observed Holiday: Presidents' Day
02/17 Details of the Hydrogen atom 1: extra [HW4 due]
02/22 Details of the Hydrogen atom 2: extra
02/24 Quantum mechanics in phase-space: §15 [HW5 due]
02/29 Scattering - general theory: §16.1-3
03/02 Born approximation and scattering operators: §16.4-5
03/07 Scattering resonances and other topics: §16.6-7
03/09 Identical particles & the Helium atom: §17 [HW6 due]
  Spring Recess: March 12th through March 20th
03/21 Once ionized Hydrogen molecule: extra
03/23 2nd Midterm Exam (§16-17, He, H2+) open-book+ take-home due Monday, 03/28, 5:00 pm
03/28 Molecular stability: extra
03/30 Many fermions, Hartree-Fock, correlations, BCS pairing theory: §18.1-5 [HW7 due]
04/04 Quantum fields, zero-point energy and the Casimir force: §19.1-3
04/06 EM field states, spontaneous emission and photon detectors: §19.4-6 [HW8 due]
04/11 Correlations, coherence and tomography: §19.7-9
04/13 Crystals and semiconductors: extra [HW9 due] --- Final Exam handed out, due Wednesay, 04/20, 5:00 pm
04/18 Crystals and semiconductors 2: extra
04/20 Quantum measurement, Bell's theorem, etc. §20 --- Final Exam due by 5:00 pm
Note: in case of class-cancellation (such as due to inclement weather), a soon Friday 2:10--3:30 pm time will be used to make-up the class

Homework assignments

  1. Due 01/20:
    1. Read the solution to 1.13, then do problem 1.14; (yes, this is indeed an assignment from Chapter 1)
    2. Assuming that η(E) = C exp[–(E/E0–1)2/2], calculate A(t) as on p. 341.
  2. Due 01/27: 12.1, 12.10, 13.1, 13.7
  3. Due 02/03: Use WKB approximation to determine the stationary state energy levels for
    1. V(x) = C|x|,
    2. V(x) = Cx2,
    3. V(x) = Cx2n, and
    4. V(x) = –C[cosh(x)]–1,
    with C > 0 in all cases, or at least determine the integral which determines these energy levels in terms of an integer.
  4. Due 02/17: 14.1, 14.2, 14.3, 14.4
  5. Due 02/24: TBA
  6. Due 03/09: 16.2, 16.3, 16.4, 16.8
  7. Due 03/30: 17.1, 17.2, 17.3, 17.6
  8. Due 04/06: 18.1, 18.4
  9. Due 04/13: 19.1, 19.2, 19.4 (just iterate the canonical commutation relations)

All homework assignments are due by 5:00 pm of the day indicated and should be either given to the instructor in hand, left in the instructor's mailbox in TKH#105, or slid under the instructor's office door, TKH#213. Late homework will not be accepted, except in cases of proven (medical) emergency.

Collaboration policy Collaboration -- but not blind copying -- on the homework assignments is strongly encouraged; students should use this to learn from each other. All exams and quizzes are open text and open class-notes (including notebooks and class handouts), but no collaboration is allowed; by signing the exams and quizzes, the student implicitly agrees to abide by this policy. Violation of this policy is covered under University regulations on academic dishonesty and cheating.

Presentation and organization While a neat presentation of home,- quiz- and exam-work is not required for full credit, it certainly makes it easier to assess the quality of the work and give the proper credit due. In all cases, include a simple sketch if it might help conveying the approach or the calculations. Where necessary, include all units and symbols such as the measure of an integral, arrow on a vector, vertical bars for the absolute value of a quantity, for the magnitude of a vector or for the determinant of a matrix, etc.

ADA disclaimer
Howard University is committed to providing an educational environment that is accessible to all students.  In accordance with this policy [details], students in need of accommodations due to a disability should contact the Office of the Dean for Special Student Services at 202-238-2420, for verification and determination of reasonable accommodations as soon as possible after admission to the Law School, or at the beginning of each semester.

Statement on Interpersonal Violence:
Howard University takes sexual assault, dating violence, domestic violence, stalking and sexual harassment seriously. If a student reveals that he or she needs assistance with any of these issues, all Responsible Employees, which includes faculty, are required to share this information with the University Title IX Office (202-806-2550) or a student can be referred for confidential services to the Interpersonal Violence Prevention Program (IVPP) (202 238-2382) or University Counseling Services (202 806-6870). For more information about these services, please go to www.CampusSafetyFirst.Howard.edu.

© Tristan Hübsch, 2016


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