PHY281S - Introduction to
Quantum Mechanics
This course will attempt to give you a basic understanding of physics at the atomic scale. We will study how atomic phenomena necessitate the use of the quantum mechanical approach. We follow the textbook closely. The text is:
An Introduction to Quantum Physics
by
A.P.French & Edwin F. Taylor
It is published by Norton in the MIT Introductory Physics Series. It is the textbook that has been used with this course over the past 6 years (at least).
The textbook takes a fairly conventional approach to quantum physics. It, and the course, are intended to provide a more in-depth study of the microscopic world than is usually given in modern physics courses, but not yet at the level of mathematical sophistication of a full quantum mechanics course. If the subject catches your interest we encourage you to delve deeper into the matter. There are many textbooks on Quantum Mechanics that you should be able to follow in parallel to our work in this course. A few that we recommend are:
1) The Feynman Lectures on Physics (Volume 3) (Addison Wesley).
2) Modern Physics by H.C. Ohanian (Prentice Hall).
3) Quantum Mechanics for Engineering, Materials Science and Applied Physics by H. Kroemer (Prentice Hall). This book is slightly more advanced.
There are also a number of popular accounts of the "meaning" of quantum mechanics:
4) QED - The Strange Theory of Light and Matter by Richard Feynman (Princeton Press).
5) The Quantum Dot - A Journey into the Future of Microelectronics by Richard Turton (Oxford University Press).
6) There are also dozens of Scientific American articles on the subject.
Bear in mind that you will only need the textbook to follow the material presented in class and to do the homework problems.
Course Outline
We plan to get through the following material. There are almost 3 weeks of "reserve". Several of the "Lectures" will take more than one class. Please don't hesitate to ask questions. We plan to review the material we have covered before the midterm and final exams. We will try to get feedback from you in various ways during the term:
a) The results of the homework assignments and discussions with TAs.
b) We encourage you to send either of us E-mail with questions/comments.
c) The results of the mid-term exam.
After each lecture is a textbook reference. Not all lectures are from the textbook and some sections of the textbook are not explicitly contained in the syllabus. None the less all the material in chapters 1 thru 5 as well as 8 and part of 9 will be of use to you in understanding the material for which you are responsible in this course. We indicate (in brackets after the lecture number) which lecturer (JW or WT) you can expect to cover the various different topics. However there may be some mixing near topic/chapter boundaries.
Lecture 1 (JW): An Introduction to Quantum Mechanics via the two slit experiment. (NA)
Lecture 2 (JW): The Classical Atom, An Introduction to the quantum length scale. (1.1-1.5)
Lecture 3 (JW): Photons, Discrete energy levels in atomic spectra. (1.6-1.9)
Lecture 4 (JW): The wave properties of particles. (NA)
Lecture 5 (JW): The deBroglie Hypothesis. (2.1)
Wave/particle velocities and the deBroglie wavelength. (2.2-2.3)
Lecture 6 (JW): The observation of the electron waves.
The Davisson-Germer experiment. (2.3-2.5)
Lecture 7 (JW): Wave-Particle duality. (2.9 - 2.11)
An introduction to the Schrodinger equation. (3.1-3.3)
Lecture 8 (JW): A simple example -- Particle in a one-d box. (3.4-3.5)
Stationary states of quantum mechanical systems. (3.6-3.7)
Lecture 9 (WT): Particle in non-rigid box. (3.8)
Square-well potential of finite depth. (3.9)
Lecture 10 (WT): Qualitative considerations of wave functions. (3.10)
Asymptotic limits, parity, superposition. (3.11)
Lecture 11 (WT): Solutions to the "real" One dimensional Schrodinger eqn.
The square well potential. (4.1-4.2)
Lecture 12 (WT): The harmonic oscillator potential. (4.3)
Vibrational energies of di-atomic molecules. (4.4)
Lecture 13 (WT): Computer solutions of the Schroedinger equation. (4.5)
Lecture 14 (WT): Midterm review (Chapters 1 to 3).
Lecture 15 (WT): Midterm exam (in class).
Lecture 16 (WT): Quantum Mechanics in 3 dimensions. (5.1-5.2)
Eigenfunctions and Eigenvalues. (5.3-5.4)
Lecture 17 (JW): Spherically symmetric solutions to Schrodinger. (5.5)
Quantization of energy levels. (5.5)
Lecture 18 (JW): Application to the Hydrogen atom. (5.5 again)
Lecture 19 (JW): Normalisation of Wave Function and Probability Density. (5.6)
Lecture 20 (JW): The Heisenberg Uncertainty Principle. (see 8.5-8.6)
Implications for deterministic measurements. (5.6-5.7)
Lecture 21 (JW): Time dependence of quantum states. (8.1)
  Superposition of states. (8.2)
Lecture 22 (JW): The motion of a particle in a box. (8.3)
Packet states in a square well potential. (8.4)
Lecture 23 (WT): Free particle packet states. (8.7)
Lecture 24 (WT): Packet states of moving particles. (8.8-8.9)
Lecture 25 (WT): The uncertainty relation for energy and time. (8.10-8.11)
Computer demonstration of solutions
Lecture 26 (WT): Scattering processes and wave packets. (9.1)
Lecture 27 (WT): Probability density and Probability current (9.3)
Lecture 28 (WT): Scattering by a one dimensional potential well. (9.4)
Lecture 29 (WT): Tunneling through a barrier. (9.5,9.7-9.8)
How a transistor works (NA)
Lecture 30 (WT): Review for final exam.
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