Physics 811   Quantum Mechanics I

                                              Spring 2009

                                                           TU 2:30-3:45pm    CW 143

 

Instructor: C. D. Lin CW230   532-1617 cdlin@phys.ksu.edu      

 

Textbook: 

I will not assign any textbook for this class. There are these standard “old” Quantum textbooks that you might have already on your bookselves.

Here are some standard textbooks:

·         Quantum mechanics, E. Merzbacher, 3rd Edition

·         Modern quantum mechanics, J.J. Sakurai,

·         C. Cohen-Tannoudji, B. Diu, and F. Laloe, Quantum Mechanics (1997)

·         Quantum Mechanics, by L. Schiff.

·         Lecture on Quantum Mechanics, by Baym.

 

There are newer Quantum Mechanics textbooks coming out recently like

                          Michel Le Bellac, "Quantum Physics",  2006 Cambridge University Press.

I like this book a lot but it appears at a higher level than we can offer. I will adopt some materials from this book but then I will give you the lecture notes.

 

At the more elementary level, the standard book I will refer to is

                         Introduction to Quantum Mechanics, by David Griffths.

I will also rely heavily on resources that are available on the web.

Class attendance

   Attendence is required. There will be short quizzes at the beginning of the class from time to time.  I will engage more discussions in the class so I can find out what the students know and do not know. You will be asked to answer questions in some random order.  The lecture will be emphasizing the concept. Detailed derivations will be avoided in the class if they can be found in standard textbooks.

Help hours:

Please reserve 5:30-7:30pm each Wednesday for help sessions. In general I will be available in my office for your individual questions during these hours. At times we will have sessions for the whole class in room 119 since it has large tables which are more convenient for discussions.

I will also use this time period for make-up lectures. 

For short questions, you can drop by my office or e-mail me first for appointment. I do encourage discussions among the students first. I prefer questions from a group of students.

   

 Grading:  

·         Short quizzes at the beginning of the class from time to time: 15%

·         two quizzes    25% each

·         final                25%

·         Homework     15%

   Examination dates:

    Exam 1:    February 24,  2:30-3:45pm

    Exam 2:   

    Final exam (comprehensive)    

Tentative Course Outline:

  In QMI we will learn basic concepts in quantum mechanics, and will restrict ourselves mostly to finite dimensional problems. Modern development of QM which leads to the so-called quantum information theory from the last two decades will be emphasized. Standard wave mechanics topics will be covered later in this semester and continued on QM2. These parts will follow mostly Merzbacher's book.

    

Materials to be covered –

Below is what I covered in 2008 spring. There will be small changes as the material is updated.

 Part A.  Elements  of Quantum Mechanics

1.       Quick review of modern  matter wave experiments

2.       Basic Principle of Q.M.

Hilbert space; Time evolution operator;  Measurements;  Complete set of commuting observables

3.       Photon polarization (Le Bellac, chapter 3)

Classical polarization; Jones vector;  polarization of a photon; projection operator.

4.       Quantum cryptography

5.       Spin 1/2 systems

Stern-Gerlach experiment; spin state of arbitrary orientation; Pauli matrices; rotation of spin 1/2  states;

6.       Density operator/State Operator (La Bellac)

Pure states; mixed states; spin polarization; dynamics and time evolution; time-dependence of state operator;

7.       Entangled states (La Bellac, chapter 6)

Two spin 1/2 systems; product space;  reduced state operators.

8.       The EPR paradox and the Bell Inequality

EPR thought experiment;  Resolving EPR paradox; Quantum Information

9.       Quantum Computing and Quantum Teleportation

Hadamard gate and CNOT gate

 

Part B. Schrodinger Quantum Mechanics

1.       Some formal quantum mechanics

General Heisenberg uncertain relation;  Time evolution operator

2.       Two-level problems—spin 1/2 particles in a magnetic field

Constant B field; NMR; resonances;

3.       Two-level problems  II

Ammonia masers; neutrino oscillator

4.       Systems with finite with finite number of levels

Molecular orbitals of C2H2; H2+, benzene

 

Part C. Practical methods of solving Schrodinger equation –Quick review of some 1D problems

1.        Spreading of a wave packet in free space

2.       1D Harmonic oscillator—operator formulation

Creation and annihilation operators; motion of a wave packet; coherent and squeezed states

    ** students are assumed to be familiar with these problems at the level of Griffths and can use Mathematica to solve problems.

For bound states, they know how to solve: infinite square well, finite square well; delta-function potential; harmonic oscillator (Chapter 2 of Griffths). They also know variational method and simple perturbation theory(Griffths 6.1 and 6.2) . For continuum states, they are familiar with scattering from steps, wells.

3.       Resonances, phase shift, time delay and scattering matrix in 1D scattering  (Merz. p97, p108)

4.       Density of states and periodic boundary conditions (Merz. P64)

Including quantum dots, quantum well, quantum wire

5.       Charged particles in an EM field; Gauge Invariance (Merz. P71-77)

6.       Part D. Three-dimensional Problems

1.       Orbital Angular momentum

2.       Algebraic approach to angular momentum

3.       Addition of angular momentum

 

 Guidelines for homework:    

    This is a course where you learn the abstract concept of  quantum mechanics and apply it to solve  problems. You are to learn mostly by doing the homework. One set of homework will be given each week on Tuesdays.  That set will be due on the following Tuesday.  The homework will be posted on my teaching webpage, or by e-mails.

    In writing your homework solutions, you should be able to explain the steps logically. You are free to discuss with other students but you have to write up your own.  Once you finish a calculation, look at the answer and ask yourself if it makes sense to you. If not, say so and why. You need to make a judgment on your results.

     Your are encouraged to use Mathematica or any equivalent tools to do the homework. However, make sure that you simplify the expressions before you go to use such tools. The expression coming out of the Mathematica should be written down separately by hand.  Write down the steps of your solution. When it comes to an integral, you can then go to Mathematica. Then copy down the result by hand.  When you are asked to graph something, label the graph carefully and the graph should be presented in a way that is clear to understand. It means that you need to judge whether it is a linear, a log-log or a semi-log plot.

 

Students with disabilities:    If you have any condition such as a physical or learning disability, which will make it difficult for you to carry out the work as I have outlined it or which will require academic accommodations, please notify me and contact the Disabled Students Office (Holton 202), in the first two weeks of the course

Plagiarism:   Plagiarism and cheating are serious offenses and may be punished by failure on the exam, paper or project; failure in the course; and/or expulsion from the University.  For more information refer to the “Academic Dishonesty” policy in K-State Undergraduate Catalog and the Undergraduate Honor System Policy on the Provost’s web page at http://www.ksu.edu/honor/