• 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 first part of the introductory course on Quantum Mechanics for first year Physics graduate students. The main topics to be discussed are: the principles of Quantum Mechanics, Wave Mechanics, Matrix Mechanics, the Dirac formulation, Transformation Theory and Symmetries.

Objectives

After completing this course the student will have a good understanding of the general principles of Quantum Mechanics and a basis to study its applications in more specific contexts.

Contents

• Survey of elementary (undegraduate) wave mechanics
  • Gaussian integrals
  • The Dirac delta function
  • Fourier series and integrals
  • One-dimensional bound state problems (particle in a box, square well, delta potential
  • Continuous spectrum, the free-particle, one-dimensional scattering
• Survey of elementary (undergraduate) matrix mechanics
  • Two-level systems
  • One-dimensional harmonic oscillator
• Mathematical preliminaries
  • Linear vector Spaces
  • The Dirac notation
  • Eigenvalue problem
  • Representations, Transformations, Matrices
• Postulates of Quantum Mechanics
  • Postulates
  • Schrodinger equation
  • Wave mechanics
  • Matrix mechanics
  • Pictures
• Angular momentum
  • Algebraic properties
  • Addition of angular momentum
• Symmetry transformations
  • Translations and lineal momentum
  • Rotations and angular momentum
  • Representations - Spin
  • Accidental symmetries
  • Internal symmetries

RIGHTS OF STUDENTS WITH DISABILITIES
ACOMODO RAZONABLE
INTEGRIDAD ACADEMICA
HOSTIGAMIENTO SEXUAL

Jose F Nieves