**PY 235 Quantum Waves**

**Dept. of Physics and Astronomy**

**Stonehill College **

Prof. Alessandro Massarotti

Stonehill College, MA &

Associate at the Harvard College Observatory

Prof. Joe J. Perez

Stonehill College, MA

Contact information:

amassaro @ cfa.harvard.edu

amassarotti@stonehill.edu

jjperez @ stonehill.edu

Textbook:

D. J. Griffiths “Quantum Mechanics” Third Edition, Prentiss Hall.

Suggested additional reading:“Physics for Scientists and Engineers”, third edition volume 1 and 2, D. C. Giancoli, Prentiss Hall publisher.

Course Description

The course is meant for students with a strong background in elementary physics. It is a natural continuation of the two elementary physics courses PY 121-122, and students who have already taken these preliminary courses plus PY 221 can automatically join PY 235. “Quantum Waves” can be taken as a stand-alone course or as part of a Learning Community, which includes Calculus III (MA 261) as well as the LC 221 “Quantum Waves” teaches about various quantum mechanical phenomena. With the creation of quantum mechanics in the 1920s, physicists conceived of a new and unexpected kind of wave that is neither a Newtonian (c. 1700) mechanical wave nor a Maxwellian (c. 1860) electromagnetic wave. These mysterious DeBroglie – Schrödinger waves of probability are the essence of quantum mechanics. These waves determine the structure of atoms and molecules, i.e. they are the deepest foundation of both physics and chemistry.

**List of Topics:**

**Blackbody Radiation**: good conductors are bad radiators; cavity as a good black body; radiation modes in a cavity; classical expected spectrum; Planck’s hypothesis of light ‘quanta’.

**Photoelectric Effect**: shining light onto a metal; classical expectations v.s. quantum.

**Electron Diffraction**: revisiting light diffraction; single and double slit patterns; classical expectations for the motion of electrons passing through slits; electron diffraction, dependence on momentum.

**The Bohr Atom**: classical electron orbits and their energy; line spectra as we see them; Rutherford’s planetary model; Bohr’s postulates and correspondence principle.

**Schrödinger Equation: **Plane waves and Wavepackets; probability interpretation of the wave function; Schrödinger equation; Heisemberg uncertainty relations; interlude on the Fourier theorem; coordinate and momentum spaces.

**Eigenvalues and Eigenfunctions**: time independent Schrödinger equation; eigenvalues; particles in a box; expansion postulate; degeneracy.

**One Dimensional Stuff**: potential step and well, general barrier; tunneling; bound and unbound states, harmonic oscillator.

**First Midterm**

**Genaral Structure of Wave Mechanics**: Hamiltonian, other observables; vector spaces and hermitian operators, simultaneous observables; classical limit.

**Operator Methods**: abstract view of QM; energy spectrum of the harmonic oscillator; re-interpretation of Schrödinger equation; time dependence of operators.

**Orbital Angular Momentum**: commutation relations; raising and lowering operators; spherical harmonics, rotational invariance.

**Hydrogen Atom**: central potential; energy spectrum; free electron; infinite spherical well; plane wave in spherical harmonics.

**Matrix Representation of Operators:** matrices in QM; matric rep of angular momentum operators; general relations.

**Spin**: 1/2 spin; addition of spins; general rules for angular momenta; spin 1/2 as a fundamental unit of quantum information.

**Time-Independent Perturbations:** energy shifts, perturbed eigenstates, spin-orbit coupling, hyperfine structure and its use in astronomy.

**Second Midterm**

**List of Miniprojects:**

1. Two-Slit Diffraction, calculation of the amplitude as a function of the angle of view.

2. Classical EM field in terms of oscillators and its quantization.

3. Quantum Description of simple solids.

4. Identical particles and Pauli’s exclusion principle.

5. Really special topic! Extra credit. The classical limit of quantum angular momentum, i.e. how we get to describe large angular momenta as simple vectors.

**Evaluation criteria:**

**Homework: 15%**: Weekly HW contains calculations based on the material presented in class. At times you will find it useful to gather information on the web. The homework can be worked out in small groups, but the draft must be individual. You also have to mention in writing the name of your partners on the HW. The grading scale is over 10 points. Late HW is accepted, but is penalized of one point per day of delay (excluding weekends), unless given explicit permission to hand in the HW late.

**Labs 20%**: Labs are group work; the size of the groups cannot be larger than three people. You submit only one report per group for grading. The report is due two lectures after you do the lab. The grading scale is over 10 points. The policy for late submission is the same as for the HW.

**Midterms: 30%**: Each midterm counts for 15% of your evaluation. The exams cover all topics presented in class up to the day before the exam, exclusive of topics already covered in the previous exam. If you cannot take the exam at the scheduled time you will arrange to take it one day earlier.

**Miniprojects/Final: 20%**:** **Five projects are listed, and you should sign up for them during the first two weeks of class, starting some research as soon as you can. The projects are a two-people enterprise. A good length for the project is of about 7 pages per person, i.e. a total of 14 pages (double space). You are encouraged to include all relevant calculations. Customarily there will be no oral presentation, just the final paper, due on the last day of class. Two points extra credit (2/20) will be automatically assigned if you give us a complete draft for feedback by April 25^{th}.

**Grades**: A > 94% A-: >89%, B+: > 84%, B > 79%, B- > 74%, C+ > 69%, C > 64%, C- > 59%, D > 49%, F <50%. I reserve the right to amend the criteria in your favor, if need comes.