Physics 6451  Quantum Mechanics I (Nieves)
 Number of Credits: 3
 Prerequisites: Permission of the Graduate Committee
 Jose F Nieves

Office: C317 (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
 Presencebased 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
 Onedimensional bound state problems (particle in a box, square well, delta potential
 Continuous spectrum, the freeparticle, onedimensional scattering

Survey of elementary (undergraduate) matrix mechanics
 Twolevel systems
 Onedimensional 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