Course Name
Paradigms in Physics: Central Forces
Course Number
PH 426 / PH 526
Year/Term
2025
Display other available years here.
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
Unit: Math Bits (PDEs)
W1 D3: Math Bits
Quantum vs. Classical Equations of Motion
Separation of Variables
Rectangular (Review)
Unit: Math Bits (Power Series Solutions of ODEs)
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
Vector Spaces/Inner Products (Review)
Undoing Separation of Variables
Quantum Cylinder
Laplace's Equation
Completeness
Lost Rows
Legendre's Associated Equation
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
W3 D1
Orbits for Inverse Square Forces
Kepler's First Law
Taylor 8.6-8.7
Unit: Quantum Mechanics on the Ring
W3 D3
Reduced Mass in Quantum Systems
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
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
W5 D1
Symmetries, Parity, Degeneracy
Orbital Angular Momentum:
Spin 1 revisited
McIntyre 7.3
Raising and Lowering Operators
Griffiths 4.3
Unit: Quantum Mechanics of the Hydrogen Atom
W5 D2
The Radial Equation
McIntyre 8.1-8.4
GCF: The Radial Equation
Final Exam
FINAL EXAM