Physics 115a: Quantum Mechanics
Winter 2001
Professor Jeffrey D. Richman
Broida Hall 5112, 8938408
http://charm.physics.ucsb.edu/people/richman/richman.html
richman@charm.physics.ucsb.edu
Quantum Mechanics
The development of quantum mechanics represents one of the greatest achievements of 20^{th} century science, requiring a radically new theoretical framework and leading to profound technological advances. Quantum mechanics is therefore one of the most exciting subjects in the undergraduate physics curriculum, and it is perhaps the most important.
Quantum mechanics is the framework we need to understand and describe the structure of matter, and its overarching principles are essential in such fields as elementary particle physics, atomic and nuclear physics, condensed matter physics, and astrophysics. Its applications are unlimited: from nuclear magnetic resonance imaging to the devices that power computers and the Internet, quantum mechanics is an indispensable tool for understanding the most important and sophisticated technological devices and for inventing new ones.
Quantum mechanics is also one of the most important and challenging courses that you will take as an undergraduate. It involves an entirely new way of thinking about physical problems from what you have encountered in classical mechanics, electromagnetism, and thermodynamics. In each of these branches of physics, there are startling examples where the classical (i.e., nonquantum) predictions fail completely to describe the observed phenomena. These observations cannot be accounted for by minor changes to classical theories; an entirely new and conceptually different set of physical principles is needed.
Goals of This Class
This class (Ph 115a) has several goals:
 To gain an understanding of the theoretical assumptions and framework of QM that will serve as a solid foundation for continued learning of the subject.
 To analyze some typical experiments that exemplify quantum behavior and to see how classical physics is unable to describe these observations.
 To analyze a variety of onedimensional quantum mechanical problems that embody a number of key quantum effects, such as tunneling.
 To analyze the relationship between classical and quantum physics: since there is an entire realm of phenomena in which classical physics works extremely well, the predictions of QM must agree with those of classical physics for these phenomena.
 To analyze the quantum harmonic oscillator, a system of great importance with extensive applications in real physical systems.
In Ph 115b and 115c, we will study many other quantum systems.
How to Succeed in This Class
Richard Feynman once said that learning quantum mechanics is like painting a house: you need more that one coat of paint. After taking this course, you will almost certainly feel that there are many aspects of quantum mechanics that you do not understand well. Because quantum mechanics is such a strange, deep, and complex subject, you could study it for a lifetime. The course that I will teach is mainly a nonrelativistic treatment; in graduate school, you typically take a more sophisticated version of the same thing, and then move on to relativistic quantum mechanics and relativistic quantum field theory. Eventually, you may even study string theory, which promises to solve one of the greatest problems of physics: how to combine quantum mechanics and gravity.
Quantum mechanics may be one of the most difficult courses you will take as an undergraduate, and it will require a high level of discipline and effort to master it. The rewards, of course, are enormous: you will have learned the language required to understand much of modern physics.
Here are some specific suggestions on how to do well in Ph 115:
 Be an active listener and a participant in lectures. It is essential to make the best use of your time in lecture. This means really paying attention, taking good notes, and asking good questions. But don’t just be a notetaker! Questions from students are usually incredibly helpful to everyone—professor and students—by helping the professor to clarify confusing points and to make sure that the most important information does not get lost in the details. Often, the best students are the ones who ask questions, since others feel that they do not know enough to ask one. I strongly encourage you to ask questions even if they are not perfectly formulated!
 Homework and problem solving is where the rubber meets the road. You have to grapple with quantum mechanics yourself. It’s perfectly fine to discuss and argue about homework problems with your friends, but make sure that you aren’t depending on others more than you should.
 You are encouraged to find other books on quantum mechanics—there is a vast number—to find alternative presentations, examples, and problems. Don’t let the class set the boundary for your learning. There is no boundary!
 Come to office hours and definitely come to the recitation section on Fridays.
 Keep up with the material. Schedule enough time for reading and homework. Students sometimes underestimate the importance of very careful, active reading.
 Because quantum mechanics is so different from the classical physics you have studied so far, you may need to spend more time than you first expect simply to think about it! Start off by allocating plenty of time in your schedule for your reading and homework.
Grades, Homework, Tests, and All That Stuff
 Homework will be assigned on Wednesdays and is due on the following Wednesday.
 Lectures: M, W 12:00—1:15 PM in Broida 2015
 Recitation section (required) F 9:00 9:50 AM in Broida 1015
 Office hours: TBA
 Grading policy:
 Homework: 40%
 Midterm: 25%
 Final exam: 35%
 Graduate teaching assistant: Blake Purnell
 Textbooks: Principles of Quantum Mechanics by R. Shankar and Essential Quantum Mechanics by P. Landshoff et al. The book by Shankar is the main text; you should study it extremely carefully. It is, however, somewhat theoretical, with not quite enough physical examples. The book by Landshoff is nice because it is very short and has some additional problems and physical examples.
 Midterm Exam Date: Weds, Feb 14, in class.
 Final Exam Date: Mon, March 20, 12 noon—3 PM (to be confirmed).
Books on Reserve
I have put a number of books in the Reserve Book Room of the Davidson Library. There is a broad range in the style of presentation, and you may find some much more helpful than others.
 C. CohenTannoudji, B. Diu, F. Laloe, Quantum Mechanics, Vols. I and II. An impressive book; rather long but extremely detailed. Often used as a textbook.
 R. Liboff, Introductory Quantum Mechanics. Used in lastyear’s course as textbook; a good book.
 A. Goswami. Quantum Mechanics. I haven’t read it, but some people think highly of it.
 D. Griffiths, Introduction to Quantum Mechanics. By a prolific textbook writer; used at many universitites. Some students complain that it does not have enough information and can be confusing.
 A. Messiah, Quantum Mechanics, Vols. I and II. A classic, somewhat advanced treatment.
 D.T. Gillespie, A Quantum Mechanics Primer. Short and easy. Helpful if you are totally confused.
 L. Landau, Quantum Mechanics. A classic; difficult.
 M. Morrsion, Understanding Quantum Physics. I haven’t read it.
 A. Migdal, Qualitative Methods in Quantum Theory. A very interesting book, with many physical examples and ingenious methods for solving them. Probably best appreciated after a quarter or two of quantum mechanics.
 J. Singh, Quantum Mechanics. A perspective from an expert on technological applications.
 G. Gamow, Thirty Years that Shook Physics. An amusing historical book, with photographs of Bohr riding a motorcycle, Heisenberg in a bathing suit, and Fermi playing tennis.
 D. Park, Introduction to the Quantum Theory. An old standby. I haven’t read it.
 A. Yariv, An Introduction to the Theory and Applications of Quantum Mechanics. A perspective from a famous laser physicist.
 P. Landshoff, A. Metherell, G. Rees, Essential Quantum Physics. A short book with some physical examples. Supplemental text for this course.
 H. Ohanian, Principles of Quantum Mechanics. I haven’t read it.
 E. Taylor and J. Wheeler, Spacetime Physics. A great book to brush up on your special relativity or to learn it for the first time. Very pedagogical and interesting.
Ph 115a: Preliminary Schedule for Winter 2001
Class 
Date 
Topics 
Chapters (Shankar=S/Landshoff=L) 
1 
Mon, Jan 8 
Mathematical Introduction 
S1/L1 
2 
Weds, Jan 10 
Math Intro 
S1/L1 

Mon, Jan 15 
MLK Holiday 
 
3 
Weds, Jan 17 
Math Intro 
S1/L1 
3.5 
Fri, Jan 19 
Math Intro 
S1/L1 
4 
Mon, Jan 22 
Math Intro;
Classical Mechanics and its Limitations 
S1/L1
S2 
5 
Weds, Jan 24 
Evidence for Quantum Behavior 
S3 
6 
Mon, Jan 29 
Postulates of Quantum Mechanics 
S4/L2 
7 
Weds, Jan 31 
Postulates of QM 
S4/L2 
8 
Mon, Feb 5 
Postulates of QM 
S4/L2 
9 
Weds, Feb 7 
Problems in One Dimension 
S5/L3 
9.5 
Fri, Feb 9 
Problems in One Dimension 

10 
Mon, Feb 12 
Problems in One Dimension 
S5/L3 

Weds, Feb 14 
MIDTERM EXAM 


Mon, Feb 19 
Presidents’ Day Holiday 
 
11 
Weds, Feb 21 
Problems in One Dimension 
S5/L3 
12 
Mon, Feb 26 
The Classical Limit 
S6/L4 
13 
Weds, Feb 28 
Quantum Harmonic Oscillator 
S7 
14 
Mon, Mar 5 
Q. Harmonic Oscillator 
S7 
15 
Weds, Mar 7 
Q. Harmonic Oscillator 
S7 
16 
Mon, Mar 12 
Q. Harmonic Oscillator 
S7 
17 
Weds, Mar 14 
Q. HarmonicOscillator 
S7 
Note: classes 4.5 and 12.5 are particularly important recitation sections.