atom QUANTUM MECHANICS I

University of Maryland at College Park, Fall of 2006

Instructor:

Dr. Paulo Bedaque

2103 Physics Building
(301) 405-6148
bedaque@umd.edu

Grader:
Haipeng An
4219 Physics Building
(301) 405-6073

Textbooks:

We will not follow any book too closely but a useful reference is

"Introduction to Quantum Mechanics", David J. Griffths.

We will have time for very little discussion of the historical develoment of the subject. I suggest you read

"Introducing Quantum Theory", by J. P. McEvoy

during the first couple of weeks (or before the classes start) in order to learn a bit about the history and also to be introduced to the subject without getting deterred by technicalities. It makes a great, light summer reading (it's a comics book !).

But different people will enjoy different books. Our library has a good collection of them for you to explore. The best book for you will be the one you like the most.

Course Policies:

Classes will meet on Mondays (10:00am), Wednesdays (10:00am and 11:00am) and Fridays (10:00am). Office hours will be from 11:00am to 12 noon, Mondays and Fridays in the instructor's office (2103 Physics Building).

We will have two exams, a midterm and a final, and periodic home problems. The grade will be based on the two exams (40% for the midterm, 50% for the final) and homework (10%).

Tentative Syllabus:

Aug. 30   Introduction to the class
Sep. 1st   Blackbody radiation
Sep. 6 Photoelectric effect, Compton scattering
Sep. 8 Bohr atom
Sep. 11 Bohr atom
Sep. 13 Matter waves
Sep. 15 Schroedinger equation, the wave function
Sep. 18 Probability and the statistical interpretation of the wave function
Sep. 20 Momentum operator and the Uncertainty Principle
Sep. 22 Free particle
Sep. 25 Infinite square well
Sep. 27 Finite square well
Sep. 29 Harmonic oscillator
Oct.  2 Harmonic oscillator
Oct. 4 Linear algebra: review
Oct. 6 Linear algebra: eigensystems
Oct. 9 Linear algebra: Hilbert spaces, Dirac notation
Oct. 11 The formalism of quantum mechanics: states, operators, observables, eigenstates, ...
Oct. 13 The formalism of quantum mechanics: states, operators, observables, eigenstates, ...
Oct. 16 The double-slit experiment
Oct. 18 Two-state systems
Oct. 20 Two-state systems
Oct. 23 Review
Oct. 25 Mid-term
Oct. 27 Mid-term discussion
Oct. 30 Scattering in one dimension
Nov. 1 in one dimension
Nov. 3 Three-dimensional Schroedinger equation
Nov. 6 Angular momentum
Nov. 8 Angular momentum
Nov. 10 Three-dimensional square well
Nov. 13 Hydrogen atom
Nov. 15 Hydrogen atom
Nov. 17 Spin
Nov. 20 Spin
Nov. 22 Fine and hyperfine structure
Nov. 27 Complicated atoms, molecular binding, chemistry
Nov. 29 Complicated atoms, molecular binding, chemistry
Dec. 1 More on chemical binding
Dec. 4 Identical particles: bosons and fermions
Dec. 6 Pauli principle and applications to atoms, metals, white dwarfs ...
Dec. 8 Quantum statistical mechanics
Dec. 11 Solids and the blackbody radiation, again
Dec. 20 Final, 8:00 AM

Homework:

Homework will be posted here, together with the solutions when available (the solutions are no longer available).

Homework 1 (due September 15, before class)    homework 1 solution
Homework 2 (due September 29, before class)    homework 2 solution
Homework 3 (due on October 11 before class)    homework_3_solution-a homework_3_solution_b homework_3_solution_chomework_3_solution_d
Homework 4 homework solution 4
Homework 5 homework_solution_5.1 homework_solution_5.2 homework_solution_3
Homework_6 homework_solution_6.0 homework_solution_ 6.1 homework_solution_6.2
Notes:
Separation of variables, spherical coordinates: 12

MIDTERM
solution

FINAL
solution 1solution 2solution 3solution 4

Interesting links:

Blackbody radiation

You can buy your own blackbody here. 

A nice figure of the blackbody spectrum.

The Universe as a blackbody: the spectrum from COBE and the tiny variations of the temperature with the direction in space. More about the COBE sattelite.

Photoelectric effect:

An applet that simulates the photoelectric effect. Try  varying the different handles and predicting the outcome !

Spectra

A beautiful picture of the absoprtion spectrum of the Sun. Part of the hydrogen, mercury and neon emission spectra and the hydrogen absorption spectrum is shown here. Notice how the emission and absoprtion spectra of the hydrogen match. Based on their wavelength, can you ideintify the hydrogen lines (meaning, find out the initial and final states of the electron emiting those photons) ?

Electron double-slit experiment

The quantum Truth before your very eyes:  Fantastic movie with a real implementation of the double slit experiment with electrons from researchers at Hitachi (courtesy of Prof. L. Orozco).

Infinite square well

I made a little  movie showing the time evolution of a NON-stationary state of the infinite square well potential. This particular state is an equal superposition of the ground and first excited states.

Wave packets

A movie I made showing two sine waves with similar velocity and wavelength (in red) interfering to make a wave packet (in blue). The two dots follow one of the waves, at phase velocity, while the other follows the top of the wave packet, moving at group velocity. The relation between wavelength and frequency is the same as in quantum mechanics so the group velocity is twice the phase velocity.

Visualize Hydrogen atom orbitals

Great visualization program for hydrogen atom wave functions, courtesy of R. Hitchcock.

Good article on Otto Stern and the discovery of spin

Others

Very useful applets (physlets) illustrating various aspects of quantum mechanics.

Cool quantum mechanics applets from the Ecole Polytechnique.

Lots of good quantum applets, courtesy of  Charles Hawkins.

Problems with solutions and study aids

Homeworks and solutions from previous years can be very useful.

An article warning of frequent conceptual mistakes often made.

More problems with solutions (some of them using material not covered in the class).