Physics 205 Reading and Homework Assignments

 

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Reading #1:  Begin reading Shankar, Chapter 1, "Mathematical Introduction."  Much of this material should appear familiar to you, but as Shankar says in his Prelude, "The first chapter is very important.  Do not rush through it.  Even if you know the math, read it to get acquainted with the notation."  Please read at least through Section 1.7 before the third lecture on Monday, September 13.  Finish the reading by Monday, September 20.

Read also Sakurai 1.1 - 1.3.

Homework #1 (due Wednesday, September 22, in class):  Shankar Exercises 1.4.1, 1.6.2, 1.6.4, 1.6.5, and 1.7.1. These are very important problems -- make sure that you understand them completely.  Ask if you have any questions.  Please remember to staple your sheets together to ensure that they don't get separated or lost in the grading process.  Thank you.  As we are posting the solution sets (with the goal of posting them on the day the homework is due) we cannot accept late assignments.

 

Reading #2:  Read Shankar, Chapter 2, "Review of Classical Mechanics," by Monday, September 27.  Don't worry if you haven't seen the Poisson bracket (PB) formulation before -- you'll get to that in your classical physics courses.  It is important for our purposes as one way to make the leap to quantum mechanics.

Homework #2 (due Wendesday, September 29, in class):  Shankar 1.8.1, 1.8.2, 1.8.3, 1.8.4, 1.8.5, 1.8.10, 1.9.2, 1.10.1, 1.10.2, and 1.10.3.  There are ten problems, but most of them have short solutions.  Note that there are some short answers to homework problems at the back of Shankar (but you will still need to supply the details of the solution.)  You may work together on homework problems, but anything you turn in should be your own work.  The homework only counts towards 20% of your overall class score, but is actually much more important than that: it provides essential practice for working exam problems, for instance.

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Reading #3:  Read Shankar, Chapter 4, "The Postulates -- A General Discussion", Sakurai, pages 24-34 (“Measurements, Observables, and the Uncertainty Relations”), and the article “Quantum Cryptography”, from “Introduction” to section II.C.2 “No-cloning theorem” by Monday, October 4. 

Homework #3 (due Wednesday, October 6, in class):  Shankar 2.1.2, 2.3.1, 2.5.4, 2.7.1, and 2.7.2.  Please staple your sheets together -- thank you.

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Reading #4: Read Shankar,  Chapter 5, "Simple Problems in One Dimension".  Please finish the reading by Wednesday, October 13.

Homework #4 (due Wednesday, October 13, in class):  Shankar 4.2.1 (three points), 4.2.2, 4.2.3, 5.1.1, 5.1.2, and 5.1.3.

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Reading #5:  Read Shankar, Chapter 6, "The Classical Limit" (which is short) and start Chapter 7, "The Harmonic Oscillator."  Please finish the reading by Friday, October 22.

Homework #5:  No homework this week.  Instead, study for the midterm exam on Monday.

Reading #6: Continue reading Shankar Chapter 7, "The Harmonic Oscillator," and read Sakurai 2.3, “Simple Harmonic Oscillator”. Please finish the reading by Monday, October 25. As Shankar says, "If you understand this chapter (Ch. 7) thoroughly, you should have a good grasp of how quantum mechanics works."

Homework #6:  (due Wednesday, October 27, in class).  Shankar 5.2.1, 5.2.2, 5.2.3, 5.2.6, 5.3.4, 5.4.2 and the following problem:

A potential for . Show that the reflection coefficients are the same for a wave of the energy  incident from the left and for a wave of the energy  incident from the right.

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Reading #7: Read Shankar, Chapters 8, "The Path Integral Formulation of Quantum Theory", and 9, "The Heisenberg Uncertainty Relations" (short chapter) by Monday, November 1. Also read Sakurai, chapter 2.5, “Propagators and Feynman Path Integrals”

Homework #7:  (due Wednesday, November 3, in class).  Shankar 7.3.1, 7.3.3, 7.3.5, 7.3.6, 7.4.1, 7.4.2, 7.4.3, 7.4.5, and 7.4.6. 

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Reading #8: Read Shankar, Chapter 10, "Systems with N degrees of freedom" by Friday, November 12. Also read Sakurai, Chapter 2.6, “Potentials and gauge transformations”. 

Homework #8:  (due Wednesday, November 10, in class).  Shankar 7.4.8, 7.4.9, 8.6.2, Sakurai 2.14 and the following two problems:

1)      Estimate the ground state energy of a particle of mass  in the potential . Estimate the numerical value of the ground state energy for an electron in such potential with .

2)      Estimate the ground state energy of an electron in the potential .  (The electron moves in three dimensional space.) Take , , where e is the electron charge. Such potential is called the “screened Coulomb potential”. It is a typical interaction potential for an electron and an impurity in semiconductors.

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Reading #9: Read Shankar, Chapter 11, “Symmetries and their consequences” and begin reading Shankar, Chapter 12, “Rotational invariance and angular momentum” by Friday, November 19. 

Homework #9 (due Monday, November 22, in class)  Shankar 10.1.1, 10.1.2, 10.1.3, 10.2.1, 10.2.3, 10.3.1, 10.3.2, 10.3.3, 10.3.4. 

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Reading #10: Continue Shankar, Chapter 12, “Rotational invariance and angular momentum”. Please read at least through section 12.5 by  Wednesday, December 1.  Also read Sakurai, Chapter 3.1, “Rotations and angular momentum commutation relations” and Chapter 3.3, “SO(3), SU(2), and Euler rotations”.

Homework #10 (due Wednesday, December 1, in class)  Shankar 11.2.2, 11.4.1, 11.4.2, 11.4.4, 12.2.1, 12.2.2, 12.2.3, 12.3.3, 12.3.5, 12.3.7 (3 points). 

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Reading #11: Finish Shankar, Chapter 12, “Rotational invariance and angular momentum” by.  Also read Sakurai, Chapter 3.5, “Eigenvalues and eigenstates of angular momentum” and Chapter 3.6, “Orbital angular momentum”.

Homework #11 (due Friday, December 10, in class)  Shankar 12.4.3, 12.5.3, 12.5.4, 12.5.12, 12.5.13, 12.6.1, 12.6.8, 12.6.9.

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