Albert's To Limitless Solution

As Taught in:

2019/2020

Level:

Undergraduate

Learning Resource Types:

=> Problem Sets

=> Notes

=> Reading Resources

Course Overview:

First, this course is divided into three parts. In the first part, we introduce the basic concepts: interpretation of the wave function, relation to probability, Schrödinger Equation, Hermitian operators and inner products. We also discuss wave-packets, time evolution, Ehrenfest Theorem and Uncertainty.

Then in the second parts. We will deals with solutions of the Schrödinger Equation for one-dimensional potentials. Also we will discuss stationary states and the key problems of a particle moving in: A circle, an infinite well, a finite square well, and a delta-function potential. We examine qualitative properties of the wave-function. the harmonic oscillator is solved in two ways: Using the differential equation and using creation and annihilation operators. Then we continue to barrier penetration and the Ramsauer or Townsend Effects.

Meantime in the third parts. We will begins with the subject of scattering on the half-line. One can learn in this simpler context the basic concepts needed in 3-dimensional scattering theory (Scattered Wave, PhaseShifts, Time Delays, Levinson Theorem, and Resonances). Then turn to 3-D central potential problems. Also we introduce the angular momentum operators and derive their commutator algebra. The Schrödinger equation is reduced to a radial equation. In addition we will discuss the hydrogen atom in detail.

Which mean, in this course in the undergraduate Quantum Physics sequence. It introduces the basic features of quantum mechanics. It covers the experimental basis of quantum physics, introduces wave mechanics, Schrödinger’s equation in a single dimension, and Schrödinger’s equation in three dimensions. In this course, we will focused on scattering and resonances. There’s another course quantum mechanics course that focused on discussion to applications to condensed matter physics.

Prerequisites:

Physics 103 – Vibrations and Waves

Mathematics – Differential Equations

Textbook:

There is no shortage of excellent textbooks on quantum mechanics. However as we progress to learn, here are some of that we can use.

Griffiths, David J. Introduction to Quantum Mechanics. Pearson Prentice Hall, 2004. ISBN: 9780131118928.

Some readings support:

Shankar, Ramamurti. Principles of Quantum Mechanics. Plenum Press, 1994. ISBN: 9780306447907. 
(A conceptual textbook with many superb explanations.)

Cohen-Tannoudji, et al. Quantum Mechanics, Vols. 1 & 2. Wiley, 1991. ISBN: 9780471164333 and 9780471164357. 
(Useful for this course as well as for Quantum Physics II and III. Many students find it too encyclopedic.)

Liboff, Richard L. _Introductory Quantum Mechanic_s. Addison Wesley, 2002. ISBN: 9780805387148. 
(A detailed and pedagogic textbook with many exercises.)

Gasiorowicz, Stephen. Quantum Physics. Wiley, 2003. ISBN: 9780471057000. 
(Efficient textbook, with plenty of material but little explanation.)

Dirac, Paul Adrien Maurice. The Principles of Quantum Mechanics. Clarendon Press, 1982. ISBN: 9780198520115. 
(Deep, hard and rewarding. Not practical during the semester.)

Ohanian, Hans C. Principles of Quantum Mechanics. Prentice Hall, 1989. ISBN: 9780137127955.

Problem Sets:

For conflicts known in advance (such as religious holidays or travel) problem sets should be turned in before the deadline. Illness or emergencies must be documented if you want to excuse a late homework. To allow for unforeseen circumstances (such as work overload, an annoying headache, forgetting to turn in the p-set on time, etc, etc.) one problem set, either an omitted set or the one with the lowest score, will be removed from the calculation of the homework average.

Sitting down by yourself and reasoning your way through a problem will help you learn the material deeply, identify concepts that are not clear, and develop the analytical skills needed for a successful career in science. If you can solve the problems by yourself, you can expect to do well on the exams. After trying to solve a problem without success, seek help from staff or classmates. Many students learn a great deal from talking to each other. Identify what was preventing you from solving the problem and then solve and write up the solution by yourself.

It is a breach of academic integrity to copy any solution from another student or from previous years’ solutions. Your solutions should be logical, complete, and legible. If you cannot present a solution clearly, it is likely that you do not understand it adequately. Graders are instructed not to give credit for unclear or illegible solutions.

The topics are:

Part 1: Basic Concepts

1. Basic features of Quantum Mechanics
2. Two-slit experiments. Mach-Zehnder Interferometer
3. Photoelectric Effect
4. Galilean Transformation of de Broglie Wavelength.
5. Matter Wave for a Particle
6. Interpretation of the Wavefunction
7. Expectation values of X
8. Momentum Expectation Values
9. Hermitian Operatiors as Observables

Part 2: Quantum Physics in One-Dimensional Potentials

10. Stationary States

11. Infinite Square Well

12. Turning Points, Semiclassical Approximations, Qualitative Features of the WaveFunction.

13. Numerical solution by the shooting method.

14. Delta Function Potential.

15. Analysis of the Differential Equation of Hermite Polynomials.

16. Scattering States Continued. Reflection and Transmission Coefficients.

17. Ramsauer Townsend Effect.

18. 1D Scattering and Phase shifts.

Part 3: One-Dimensional Scattering, Angular Momentum, and Central Potentials

19. Resonances and Breit-Wigner Distribution.

20. Central Potentials and Angular Momentum.

21. Algebra of Angular Momentum

22. Quantum Associated Legendre Polynomials

23. Radial Equations

24. Begin Hydrogen Atom

25. 2-Body Problem and Separation of Variables.

26. Scales in the Hydrogen Atom.

27. Differential Equation-Behaviors at Infinity and at Zero.

28. Energy Levels Diagram for Hydrogen.

29. More on Orbits and Turning Points.

30. The Simplest Quantum System and Discovering Spin

The Readings in this Course delivered in the beginning of term, please sent me an email if you don’t get any:

1. Key Features of Quantum Mechanics: Linearity of the Equation of Motions
2. Experiments with Photons
3. Particle Nature of Light and Wave Nature of Matter
4. de Broglie Wavelength and Galilean Transformations
5. Equations for a Wavefunction, Schrödinger Equation for Particle in a Potential
6. Normalization and Time Evolution. The Wavefunction as a Probability Amplitude.
7. Wavepackets and Uncertainty, Wavepacket Shape Changes.
8. Uncovering Momentum Space
9. Observables and Hermitian Operators
10. Solving the Time-Independent Schrödinger Equation
11. The Infinite Square Well
12. General Properties, Bound States in Slowly Varying Potentials
13. Delta Function Potential
14. Algebraic Approach to the Simple Harmonic Oscillator
15. Scattering States and the Step Potential
16. Resonant Transmission in a Square Well
17. Scattering in One Dimension
18. Levinson’s Theorem
19. Quantum Mechanics in 3D and Central Potentials
20. Hydrogen Atom

I have no fans of the paper exams. However, the condition made us do a paper exam. Therefore this is an open-book exam that needs to be solved within the time frame by the end of each quarter in the course.

There are ten problem sets, two essential exams, and one final exam.

Please ask for the link once you are ready. You have a limited time to get started once you click the link sent to your email.