Course Name
Paradigms in Physics: Central Forces
Course Number
ph426
Year/Term
Spring-2025
Course Credits
3
Class meeting times
7 hours of lecture/discussion per week for five weeks.
Prerequisites
PH213, PH425, PH422
Course description
Gravitational and electrostatic forces; angular momentum and spherical harmonics, separation of variables in classical and quantum mechanics, hydrogen atom.
Topic/Day
Activities
Resources
Homework Due
W1 D1: Math Bits
Compare ISW to the Wave Equation
W1 D2: Math Bits
W1 D3: Math Bits
Quantum vs. Classical Equations of Motion
Separation of Variables
Rectangular (Review)
W1 D4: Math Bits
Series Solutions for Legendre Polynomials
Theorems about Power Series Solutions
Power Series Solutions
around Singular Points
(Frobenius Series)
W1 D5: Math Bits
Undoing Separation of Variables
Completeness
Unit: Classical Mechanics Orbits
W2 D1
Center of Mass
Survivor Outer Space: A kinesthetic approach to (re)viewing center-of-mass
W2 D2
Systems of Particles
GCF: Systems of Particles
Taylor Chap. 3 (Optional)
Central Force Lagrangians
Reduced Mass
GCF: Reduced Mass
Taylor 8.2
W2 D3
Solutions of the Harmonic Oscillator Equation (Review)
Angular Momentum
Conservation of
Classical Angular Momentum
W2 D4
Equations of Motion
Change of Variables
Polar Graphs
Circles, Ellipses, Hyperbolas
Orbit Shape
W2 D5
More Effective Potentials
W3 D1
Effective Potentials
Acting Out Effective Potentials Effective Potentials
Taylor 8.4 (Optional)
GCF: Effective Potentials
W3 D2
Orbits Summary
Unit: Quantum Mechanics on the Ring
W3 D3
Time Dependence Review
Time Evolution Refresher (Mini-Lecture) Time Evolution of the ISW
Separating out Center-of-Mass: Quantum
GCF: Reduced Mass
McIntyre 7.1
Eigenstates on a Quantum Ring
GCF: Motion on a Ring
McIntyre 7.5
W3 D4
Normalization of Eigenstates on the Ring
W3 D5
Meaning of the Wave Function
W4 D1
MEMORIAL DAY
No Class
Unit: Angular Momentum in Quantum Mechanics
Introduction to the Unit
Learning Outcomes
W4 D2
Quantum Ring with Separation of Variables
McIntyre 7.5
Schrödinger's Equation:
Spherical Symmetry
W4 D3
Spherical Harmonics:
Properties
GCF: Spherical Harmonics
McIntyre 7.6.4
W4 D4
W4 D5
W5 D1
Symmetries, Parity, Degeneracy
Unit: Quantum Mechanics of the Hydrogen Atom
Introduction to the Unit
Learning Outcomes
W5 D2
The Radial Equation
McIntyre 8.1-8.4
GCF: The Radial Equation
W5 D3
W5 D4
Visualizing Radial Functions
Visualizing Radial Wave Functions
Hydrogen Atom Wave Functions
Hydrogen Spectra
McIntyre 8.3
Hydrogen Atom Visualization of Probability Densities
Visualization of Quantum Probabilities for the Hydrogen Atom
W5 D5
Final Exam
FINAL EXAM