• Number of Credits: 3
• Prerequisites: Permission of the Graduate Committee
• Jose F Nieves
• Office: C-317 (ext 4775)
  University of Puerto Rico - Rio Piedras Campus
  Department of Physics

Text

• Principles of Quantum Mechanics, R. Shankar (Plenum Press)

Bibliography

• Messiah, A. (1961). Quantum Mechanics. Interscience, NY
• Merzbacher, E. (1970). Quantum Mechanics, 2nd ed. Wiley, NY
• Schiff, L. I. (1968). Quantum Mechanics, 3rd ed. McGrawHill, NY

Minimum Required Facilities

• Traditional lecture room

Instructional Strategy

• Lectures

Modality

• Presence-based classroom course

Student Evaluation

• Standard A to F grading system. Grading will depend on performance in periodic problem sets, a midterm exam and a final exam, with the following weights:
• Homework: 40%
• Midterm exam: 30%
• Final exam: 30%

Homeworks

By all means you may work in groups on the homework assignments. Collaboration is an important part of learning and of scholarship in general. However, each student must turn in her or his own writeup of the solutions. If two individual writeups are nearly identical, neither will receive credit. In fairness to your fellow students, late homework will not be accepted.

Description

This is the second part of the introductory course on Quantum Mechanics for first year Physics graduate students. The main topics to be discussed are: Time-independent and time-dependent perturbation methods, scattering theory, radiative decays of atoms, systems of identical particles, spin and statistics.

Objectives

After completing this course the student will have a good background to carry out basics quantum mechanical calculations in systems of practical interest.

Contents

• Time-independent perturbation theory for nondegenerate states: energy eigenvalues and eigenvectors through second order
• Time-independent perturbation theory for degenerate states: lifting degeneracies.
• Applications:
  • Simple examples: two-state systems, a simple harmonic oscillator
  • The fine structure of hydrogen: relativistic and spin-orbital effects.
  • The hydrogen atom in a magnetic field: the Zeeman effect.
  • The hydrogen atom in a electric field: the Stark effect.
• The adiabatic theorem
  • Application to spin in a time-varying magnetic field.
  • Resonant adiabatic transitions and the Mikheyev-Smirnov-Wolfenstein solution to the solar neutrino problem
• Time-dependent perturbation theory
  • General expression for transition probability
  • The Fermi Golden Rule
  • The density of states
  • Emission and absorption of light
  • Spontaneous emission. How excited states of atoms decay
• Scattering
  • Definition of the total and differential cross section
  • The Optical theorem
  • The Born approximation
  • Yukawa and Coulomb scattering
  • Scattering length
  • Resonances
• Quantum Computing
  • Qbits
  • Entanglement
  • Quantum Fourier Transforms
  • Using many two-state systems as a quantum computer

RIGHTS OF STUDENTS WITH DISABILITIES
ACOMODO RAZONABLE
INTEGRIDAD ACADEMICA
HOSTIGAMIENTO SEXUAL