Howard University
WASHINGTON DC 20059

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

Quantum Mechanics I,  PHYS-220 (80270)
        MW, 2:10- 3:30 pm, in TKH 103;
[ Topics ][ Minimal Requirements ][ Assignments ][ e-Gear ][ Welcome ]

Instructor: Tristan Hübsch (Office hours: MW 10:00 am–12:00 noon, T 2:00–4:00 pm)
TKH 213, 806-6267 thubsch@mac.com
 
Textbook and other sources (also @ iTunes U):
required: L.E. Ballentine, Quantum Mechanics
(recommended): S. Flügge, Practical Quantum Mechanics (Springer-Verlag) (try )
(optional): C. Cohen-Tannoudji, B. Diu & F. Laloe, Quantum Mechanics
(optional): E. Merzbacher, Quantum Mechanics (3rd ed.)
(optional): D. Bohm, Quantum Mechanics
and other sources, as given in class
(introductory level, optional): D.J. Griffiths, Introduction to Quantum Mechanics [errata]
Component
Time
Remark
% of Grade
Homework See in daily schedule Late HW = 0 credit !!!
30%
Exams (two midterms) See in daily schedule not comprehensive
(each) 30%
Now drop from the above three component the one with worst result for each student separately
-30%
Final exam Last week of semester comprehensive
40%

The aim of the course is to give a thorough introduction to the quantum nature of Nature, some of the basic methods and techniques in its study and to serve as a preparatory course for the second part (PHYS-221). This course begins with reviewing the experimental indications of the quantum nature of Nature. The study of basic general properties and simple 1-dimensional models introduces the basic ideas and prepares for the study of semiclassical and operatorial techniques in Quantum Mechanics. The study of angular momentum and spherically symmetric potentials then finishes this first part of the course in Quantum Mechanics.

A successful student is expected to demonstrate a very good understanding of the fundamental principles of quantum physics, but also to demonstrate-and maintain-the ability to solve practical problems involving quantum phenomena. For minimal requirements, see below!

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


Topical schedule:
§1+
Mathematical Prerequisites and Introduction to Quantum Nature
§2+
Formulations of Quantum Mechanics
§3
Kinematics and Dynamics
§4+
Coordinate Representation and Applications
1st Midterm exam--§1-4: 10/08 (open text, in-class) + take-home due 10/15
§5
Momentum Representation and Applications
§6
The Harmonic Oscillator
§7
Angular Momentum
2nd Midterm exam--§5-7: 11/12 (open text, in-class) + take-home due 11/17
§8
State Preparation and Determination
§9+
Measurement and State Interpretation
§10+
Bound States
§11+
Charged Particle in a Magnetic Field
Final exam -- comprehensive: §1-10; take-home, given 12/01, due 12/08.

Day-to-day schedule: Students are required to read ahead
08/25
The Quantum Nature of Nature: Quantum Waves and Superposition: extra
08/27
Linear Vector Spaces, Linear and Self-Adjoint Operators: §1.1-3
09/01
Observed Holiday: Labor Day
09/03
Hilbert Spaces and Probability Theory: §1.4-5 [HW#0 due]
09/08
Formalism of Quantum Mechanics: §2
09/10
Transformations, Symmetries and Identification: §3.1-4 [HW#1 due]
09/15
Quantization and Compositeness, Equations of Motion and Conservation Laws: §3.4-8
09/17
The Schrodinger Equation and Probability, The Free Particle: §4.1-6 [HW#2 due]
09/22
Sequentially Constant Potentials: extra
09/24
Tunneling and Path Integrals: §4.7-8 [HW#3 due]
09/29
Momentum Representation, Bloch's Theorem and Linear Force Field, §5.1-6
10/01
The linear harmonic oscillator: §6
10/06
The Angular Momentum Formalism: §7.1-3 [HW#4 due]
10/08
1st Midterm (§1-4; 90-min. in-class & take-home, due Wednesday, 10/15/14, 12:00 noon)
10/13
Observed Holiday: Columbus Day
10/15
Spin, Finite Rotations and Addition of Angular Momenta: §7.4-7 [HW#5 due]
10/20
Tensors, Wigner-Eckart Theorem and Rigid Bodies: §7.8-9
10/22
State Preparation and Determination, Composites and Indeterminacy: §8.1-4 [HW#6 due]
10/27
Measurement, Interpretation of a State Vector and Caveats: §9.1-4
10/29
Recombination and Conditional Probabilities, and The Measurement Conundrum: §9.5-6 & extra [HW#7 due]
11/03
The Spherical Potential Well and the Hydrogen Atom, §10.1-2
11/05
Indeterminacy and Strange Bound States, §10.3-4 [HW#8 due]
11/07
Last day to withdraw from a course
11/10
Review
11/12
2nd Midterm Exam (§5-9; 90-min. in-class + take-home, open-book,due Monday, 11/17/14, 12:00 noon)
11/17
Stationary State Perturbation Theory, §10.5
11/19
Variational Method, §10.6 [HW#9 due]
11/24
Classical vs. Quantum Theory and Motion in Uniform Static Magnetic Field, §11.1-4
11/26
Classes suspended at noon—no class [HW#10 due by 12:00 noon]
11/27–11/30: Thanksgiving recess
12/01

The Paschen-Back effect and general cases: §11.5 & extra Final Exam handed out, due: Monday, 12/08/14, 12:00 noon

12/03
Review [HW#11 due],

Minimum requirements :

To pass the course with a grade B or better , a graduate Student must, at the time of (on) the final exam, be able to demonstrate the ability to:

1
determine the type of the state (oscillatory vs. non-oscillatory), the boundary- or periodicity-matching conditions on it
2
determine the type of the energy spectrum of a particle, depending on the potential
3
complete any commutator calculation with either abstract operators, harmonic oscillator creation and annihilation operators, or angular momentum operators
4
determine perturbative corrections to energies and state-functions of stationary states
5
determine the total symmetry, degeneracy and relations between these for simple 1,- 2- and 3-dimensional systems

A graduate student who cannot demonstrate the above listed skills at the time of the final exam automatically forfeits a grade of B or better -- regardless of the total number of points acquired in homework, quizzes and exams, and regardless of the success in completing any other course requirement.


Homework assignments (49 problems)
Due
Ch. 
Problems
09/03 Assigned in class, on the first day of class
09/10
1.
2, 4, 6, 9, 12 (see soln’s of 10 and 11)
09/17
2.
1, 8, 9
09/24
3.
5, 6, 8, 10, 12
10/06
4.
1, 2, 3, 7, 9
10/15
5.
1, 2, 3, 5, 8
10/22
6.
1, 2, 6, 7, 8
10/29
7.
1, 3, 4, 8, 9
11/05
8.
1, 4, 5
11/19
9.
1, 2, 4
11/26
10.
1, 2, 3, 13, 14
12/03
11.
2, 3, 4, 8, 10

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 the University regulations on academic dishonesty and cheating.

Coursework 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.

However, as all of the above are by definition forms of the Student’s communication with the instructor, unambiguous legibility is mandatory. This requires making complete sentences and statements, choosing words and phrases precisely, and using correct punctuation; part of the credit is earned by fulfilling this task. (Consider it also as practice for communication to the scientific community and wider.)

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.

© Tristan Hübsch, 2014


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