PH426: Paradigms in Physics, Central Forces

Winter 2011

This course is taught by Prof. Ethan Minot during weeks weeks 8, 9 and 10 of Winter Quarter 2011. “Central Forces” is the 6th part of a 9 part sequence called Paradigms in Physics.

Calendar

DayTopicSummaryAdditional ReadingAssignments
1*MTwo-body ProblemsClassical Angular Momentum week1notes.pdfStart hw1
2TuDescribing trajectories in polar coordinatesworksheet: polar acceleration, worksheet: conic sections, Maple9: conic sections
3WEquations of motion hw1soln.pdf
4ThOrbit shapesWorksheet: Orbits and Maple14: Orbits Start hw2
5FInverse square force lawspractice_questions_for_final.doc
DayTopicSummary Additional ReadingAssignments
6MSchrödinger's EqnRecent Expt: Buckyball interference patternQM course packet 7-1 to 7-7hw2soln.pdf. Start hw3
7TuQuantum States on a Ring Worksheet: QM Ring7-7 to 7-28
8*WTime Dependence on a Ring Maple14: QM Ring, Recent Expt: Electrons in a metal ring hw3soln.pdf, Start hw4
9*ThLegendre's EquationMaple14: Guess Legendre, Maple11: Find Legendre Coefficients
10*FSpherical Harmonics hw4soln
DayTopicSummary Additional ReadingAssignments
11MSpherical HarmonicsMaple14: Plot spherical harmonics, Start hw5
12TuQuantum States of the Rigid Rotor Maple14: YLM Combinations
13WRadial FunctionsMaple14: Radial wavefn hw5soln.pdf, Start hw6
14ThHydrogen Atom Wave FunctionsMaple14: Hydrogen Visualization
15FThe Classical Limit + Review Practice questions for final hw6soln

*Classes on these days will be run by Corinne Manogue, Ethan Minot will be travelling.

Maple14: Effective Potential

Syllabus

Classical Mechanics
  • Systems of Particles
    • Center of Mass
  • Two-body Problems
    • Central Forces
    • Reduced Mass
  • Classical Angular Momentum
    • Torque
    • Conservation of Angular Momentum
    • Kepler's Second Law
  • Spherical Coordinates
  • Velocity and Acceleration in polar coordinates
  • Circles, Ellipses, Hyperbolas
    • Conic Sections
  • Equations of Motion: F = ma
  • Orbit Shapes
    • Inverse Square Forces
    • Kepler's first law
  • Equations of Motion: E = T + U
  • Effective Potentials
  • Other Force Laws
Quantum Mechanics
  • Schrödinger's Eqn.
    • Spherical Symmetry
    • Separation of Variables
  • The Ring
    • z-component of angular momentum
    • Degeneracy
    • Comparison to Particle in a Box
  • Quantum States on a Ring
    • Time Dependence on a Ring
  • The Rigid Rotor
  • Legendre's Equation
    • Change of Variables
    • Series Solutions
    • Legendre Polynomials
    • Rodrigues' formula
    • Graphs
    • Orthonormality
    • Legendre Polynomial Series
    • Legendre's Associated Equation
    • Legendre Functions
  • Spherical Harmonics
    • Orthonormality
  • Spherical Harmonics
    • YLM's
    • Symmetries, parity, degeneracy
  • Quantum States of the Rigid Rotor
    • Linear Combinations of YLMs
  • Angular Momentum
    • Commutation Relations
  • Orbital Angular Momentum
    • Raising & lowering operators
    • Spin 1 revisited
  • The Radial Equation
    • Radial Functions
    • Asymptotic Behavior
    • Laguerre polynomials
  • Hydrogen Atom Wave Functions
    • Symmetries, parity, degeneracy
    • Probablility Densities
  • Applications
  • The Classical Limit