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Advanced Quantum Mechanics

Advanced Quantum Mechanics

PHYS3505 3 hours

Advanced Quantum Mechanics

This quantum mechanics course explores fundamental concepts and mathematical formalisms. Topics include the addition of angular momenta, identical particles, approximation methods for stationary and time-dependent states, and scattering theory. Students will delve into perturbation theory, variational principles, transition probabilities, and interaction with radiation. Through mathematical derivations and applications, students will gain a deep understanding of quantum systems and prepare for advanced research in physics and related fields.
PHYS3504 Quantum Mechanics
3 hours

One requisite

Addition of Angular Momenta
• Addition of Two Angular Momenta: General Formalism
• Calculation of the Clebsch–Gordan Coefficients
• Coupling (addition) of Two Spin Angular Momenta
• Coupling (addition) of Orbital and Spin Angular Momenta 6

Identical Particles
• Many-Particle Systems: Schr?dinger Equation, Interchange symmetry
• Identical Particles in Classical and Quantum Mechanics
• Exchange Degeneracy
• Symmetrization Postulate, Symmetric and Antisymmetric Functions
• The Pauli Exclusion Principle, Periodic Table of Chemical Elements

Approximation Methods for Stationary States
• Time-Independent Perturbation Theory
a. Nondegenerate Perturbation
b. Degenerate Perturbation Theory
c. Fine Structure and the Anomalous Zeeman Effect
• The Variational Principle 9

Time-Dependent Perturbation Theory
• General Formulation
• Transition Probability
• Transition Probability for a Constant Perturbation
• Transition Probability for a Harmonic Perturbation
• Application: Interaction of Atoms with Radiation
a. Transition Rates for Absorption and Emission of Radiation
b. Transition Rate within the Dipole Approximation
c. The Electric Dipole Selection Rules 12

Scattering Theory
• Scattering and Cross Section
• Scattering Amplitude of Spinless Particles
• The Born Approximation
• Partial Wave Analysis