Physics 827  (Autumn 2010)

Quantum Mechanics I

Grad students from Math, Chem. and Engg. are welcome.

Prerequisites:   Some exposure to simple ideas of quantum and atomic physics at the undergraduate level would be most helpful, though it is not a strict prerequisite.   I will assume that the students have previous knowledge of mathematical methods (like matrices, simple  differential equations, etc.) used in undergraduate physics and math classes.

Students will need to know special functions (e.g., Legendre polynomials, spherical harmonics, Bessel functions) and solution of partial differential equations for Phys 828 and 829. These topics will be covered by Prof. Heinz in his E&M class Phys 834 in Au 2010.

Syllabus: Here is an outline of topics to be covered in the first quarter.

• Inadequacy of Classical Mechanics: stability of the atom; two-slit experiments.
• Mathematical preliminaries: review of linear algebra and introduction to Hilbert spaces. (I will stress applications to physics, and  not mathematical rigor.)
• Postulates of QM. States, superposition principle, operators & observables, time-evolution, measurement; uncertainty relations
• One-dimensional problems: free particle, bound states, scattering, and tunneling.
• Harmonic Oscillator.
• Two-level systems.

The Text Book for Physics 827, 828 and 829 will be                                   

"Principles of Quantum Mechanics" (2nd Edition) by R. Shankar, (Springer, 1994) [ISBN 0-306-44790-8] 

Although I will follow Shankar's development of the subject in general, I may also deviate from the book on several points, most particularly in the discussion of two-level systems and some elementary ideas about quantum computation.                        

Other useful references:

"Quantum Mechanics" Vols. I & II by C. Cohen-Tannoudji, B. Diu and F. Laloe, (John Wiley & Sons, NY, 1977).

"Lectures on Quantum Mechanics" by G. Baym, (W.A. Benjamin, NY, 1969).

"Feynman Lectures on Physics" Vol. III by R.P. Feynman, R.B. Leighton and M. Sands, (Addison Wesley, Reading, Mass., 1965).

Grading: 

• Home work: 30%  
• Mid-term exam: 30%;
• Final exam 40%

Exam Schedule:

• Mid-Term Exam: Friday, Oct. 29, 1:30 PM - 3:18 PM in Smith 1048
• Final exam: Wednesday, Dec. 8, 1:30 PM - 3:18 PM in Smith 1048

All Examinations will be closed-book and no notes will be permitted.

Office Hours: Thursdays, PRB 2024 8:30 - 9:30 AM (or by appointment)

Home Work Assignments   

Home work will be assigned on a regular basis throughout the quarter.

Homeworks should be placed in the grader's mailbox in PRB.

Grader:  Naveen Ramalingam, Room PRB 3012 (ramalingam.10@osu.edu)

You will be able to download the problem sets from here as they are available. 

outline

HW#1

HW#2

HW#3

HW#4    (due: Monday, Oct. 25 in class)

No homework in the week of Oct 25. Mid Term Exam: Oct. 29.

HW#5    (due: Friday, Nov. 5)

HW#6    (now due: Monday, Nov. 15)

HW#7    (due: Monday, Nov. 22)

Here are some extra problems that go beyond the material covered in class.

These problems will not be graded and students are not required to master them for Ph 827

extra problems#1