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Physics 311: Introduction To Quantum Physics I

 

Course Outline


Stern-Gerlach experiments: The quantum state vector

Rotation of basis states: Beginnings of matrix mechanics, rotation operators, identity and projection operators, matrix representation of operators, changing representations, expectation values

Angular momentum: Commuting operators, eigenvalues and eigenstates, raising and lowering operators, uncertainty relations

Time evolution: The Hamiltonian and the Schroedinger equation, time dependence of expectation values, precession of spin ½ in a magnetic field, magnetic resonance, energy-time uncertainty relation

System of spin ½ particles: Basis states for two spin ½ particles, hyperfine splitting, addition of angular momenta for two spin ½ particles, EPR paradox, Bell inequalities

Wave mechanics in 1D: Position eigenstates and the wave function, translation operator, generator of translations, momentum operator in the position basis, momentum space, Gaussian wave packet, Heisenberg uncertainty principle, particle in a box, scattering in one dimension

1D harmonic oscillator: Operator methods, raising and lowering operators, position space wave functions, zero point energy, classical limit, time dependence

Wave mechanics in 3D: Translational invariance and conservation of linear momentum, rotational invariance and conservation of angular momentum, a complete set of commuting observables, position space representation of the angular momentum operator, orbital angular momentum eigenfunctions, Coulomb potential, infinite spherical well

 

Organization

Lectures M W F 10:00 - 10:50 AM

Homework (30%) Weekly problem sets

Term exam (30%)

Final exam (40%)

Text: John S. Townsend, A modern approach to quantum mechanics

 

All information is representative only, and is likely to change from year to year.