News

Thursday, August 26
Class has started. The first set of notes on Lagrangian mechanics and the quantum mechanical path integral has been handed out.

An important prerequisite for quantum mechanics is a knowledge of linear algebra. You are asked to review the topic within the first two weeks of the course. An excellent overview of the linear algebra is provided as a first chapter of the recommend ed textbook, i.e., Shankar "Principles of Quantum Mechanics 2nd Ed".

Tuesday, September 7
There will be a Mathematica Tutorial given by Guochun Shi 8-9am in Loomis 144. The tutorial will explain how physics graduate students can get access to workstations in the Physics Department and in the College of Engineering, how Mathematica can be star ted on the workstations, how results can be printed. The tutorial will also give a very brief introduction to Mathematica and references to web-based tutorials.

Problem set 1 has been handed out.

Thursday, September 9
There will be a quiz in class on linear algebra, based on the chapter in Shankar.

Saturday, September 11
We have made available the quiz on linear algebra and the solutions. You are strongly encouraged to look at the material and study the topic more carefully in case that you had difficulties with the quiz. In fact, you need to know the topics asked and the other topics covered in the first chapter of Shankar "in your sleep" to be able to master quantum physics. It's better to learn this now then to fight gaps in your knowledge of the basics later.

Sunday, September 12, 1999
There is an error in Eqs. (2.109-2.111) of the notes. Please replace tau by (tau - t0) in (2.109-2.111) on the RHS. The remainder of the notes seem to be ok. Thanks to James and Mike for having pointed this out. K.S. apologizes.

Tuesday, September 14, 1999
Tuesday, Sept. 21, 1999
Dom Ricci brought to our attention an error in problem set 2. In equation 5, in part d, one of the two F(s) functions inside the double integral should be be F(tau). Thanks, Dom.

Wedesday, Sept. 22, 1999
From the students who came to my office today, I know that some of you have difficulty in homework set 2. Please feel free to come to loomis 313 in the office hours or email pinaki/me to arrange an appointment whenever you find difficulty or error(s) in the homework/lecture notes. We are always ready to answer your questions.
By the way, the homework set 2 is due next Tuesday, Sept. 28
Guochun
Tuesday, Sept. 28, 1999
Wednesday, Sept. 29, 1999
Please note: Homework should be placed in the 480 box BEFORE the lecture. Solutions of the homework will be available in the web AFTER the lecture.

Thursday, Sept. 30, 1999
Problem set 3 has been modified. Problem 5 has been shortened, eliminating the previous items 5d) - 5f). Inconsistencies in Problem 3 have been repaired (numbering (a-d, indices corrected; thanks go to Jeff for catching this). KS apologizes.

Monday, Oct. 4, 1999
Problem set 3 has been modified once more, repairing a crucial error in Eq. (1,2) [second factors in all three terms should be a sin() rather than a cos()] that had been pointed out by Jordan Vincent already yesterday. Since I used myself a correct version of the formula I did not realize the error until now and the TA, responsible for the problem set, did not report anything. Thanks Jordan and forgive me all for the frustration caused.

Thursday, October 7, 1999

Friday, October 8, 1999

Monday, October 18, 1999
Some students have problems calculating functions recursively with Mathematica. You may either choose to calculate functions one step at a time or use
Clear[h, phi];
h[y_, 0] = Exp[-(y y)/2];
h[y_, n_] := (y*h[y, n - 1] - D[h[y, n - 1], y]);
hermite[y_, n_] := Simplify[h[y, n]]*Exp[y^2/2];
phi[y_, n_] := (1/Sqrt[(2^n)* n! Sqrt[Pi]])*Simplify[h[y, n]];
Do[Phi[x_, n] = phi[x, n]; Print[Phi[x, n]], {n, 0, 4}];
Plot[{Phi[y, 0], Phi[y, 1], Phi[y, 2], Phi[y, 3], Phi[y, 4]}, {y, -3, 3}];

Tuesday, October 19, 1999

Wednesday, October 20, 1999
At the request of one of you, I have posted the details of the algebra for Problem 4c of Problem Set 3 as an Appendix. Pinaki.
The example of the semiclassical and numerically exact description of stationary states in a potential x^4 have been posted along with the lecture notes as Stationary States in x^4 Potential.

Saturday, October 23, 1999
I have received the following mail from Jordan Vincent, the answer to which I would like to bring to everybody's attention. I hope that Jordan does not mind making his inquiry public.

From: Jordan Vincent
Date: 1999-10-23 19:48:32 -0500
To: Klaus Schulten
Subject: Re: homework 5

Hello Dr. Schulten, I am still having some trouble getting Prob. 1) to work, no one so far seems to have gotten it. I get an integral of the form (c*c-u*u)^(1/2)/(u+1), where c is a constant and u is the independant variable. Could you atleast tell me if I am on the right track. Thank you, Jordan

Dear Jordan:

You are on the right track, but as usual there are several ways to solve the problem.

I actually stopped myself changing the integration variable after the z = exp(-ay) transformation. You apparently chose a transformation z = exp(-ay) -1. Both should work, your approach being probably a litle bit easier than my own.

Now you need to solve your integral, as stated by you, looking into integral tables. My suggestion is to look at "Tables of Integrals, Series, and Products" by Gradshteyn and Ryzhik (should be available in the Loomis library) where integrals of the req uired type are solved [section 2.28]. A little stroll through "algebra land" and neat book keeping should get you to the final result as stated in the problem set. On your way, you need to realize that the expression you obtain for the indefinite inte gral assumes a simple form for the integration limits specific for this case.

Best wishes on your algebra trip, Klaus Schulten

Sunday, October 24, 1999
A form Your Comments has been added to the web site that provides an opportunity for you to send comments back to me regarding the course or to send inquiries. The procedure will permit you to remain anonymous in doing so. KS

Tuesday, October 26, 1999

Wednesday, October 27, 1999
As announced in class, the midterm exam will be Thursday, November 4 in class. The exam will be open book. You can also bring the lecture notes, but you cannot bring solutions to the problem sets, neither your own nor those provided by us.

Monday, November 1, 1999
In Eq. (5.49) the minus sign in front of theta_1 should be deleted and the comment given in brackets below the equation discarded. Thanks to Mike for pointing this out.

Wednesday, November 3, 1999
HW 5 will be available during office hour today. You can pick them at 313 LLP from Guochun.
Solutions for the Problem set 6 Problem 1 and Problem 2 are now available.

Tuesday, November 9, 1999
Solutions for the Problem set 7 will be posted on Thursday, November 11.

Thursday, November 11, 1999
Solutions for Problem set 7 are available.
Problem set 8 has been altered correcting an error in Problem 4, Eq. (11). Also Problem 4 (b) has been shortened.

Friday, November 19, 1999

Tuesday, November 22, 1999

Thursday, December 2, 1999

Final Exam
The final exam for the course is on Saturday, Dec.18 from 1:30 to 4:30pm in 144 LLP.

Friday, December 10, 1999
HW 9 will be distributed today in your mailboxes. Those who do not have a mailbox in the Physics dept. should contact Pinaki.