# Central Forces Winter 2009

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Copies of the course notes can be found here:

Day Topic:
Subtopic
(Main, Alternate,  Deep)
Due Dates
1
Mon
2/23
Introduction
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
T 1.1-1.2, 1.4
Class Notes 1-3
T 3.3, 10.1

T 8.1
T 8.2
Class Notes 4

T 3.1, 3.4-3.5, 10.1

2
Tue
2/24
Spherical Coordinates
Velocity and Acceleration
Worksheet: Vel. & Acc.-Polar Coords.
Circles, Ellipses, Hyperbolas
Maple: Conic Sections
Worksheet: Conic Sections
Class Notes 5
Class Notes 6

3
Wed
2/25
Equations of Motion: F=ma
T 8.3

HW 1
Solutions
4
Thu
2/26
Orbit Shapes
Inverse Square Forces
Kepler's first law
Equations of Motion: E=T+U
Effective Potentials
Maple: Effective Potentials
Worksheet: Effective Potentials
Class Notes 7-9

T 8.4

5
Fri
2/27
Inverse Square Forces
Orbits
Maple: Orbits
Worksheet: Orbits
Visualize orbits
Other Force Laws
Orbits Summary
Recap
T 8.5-8.7

HW 2
Solutions
6
Mon
3/2
Schrödinger's Eqn.
Spherical Symmetry
Separation of Variables
Class Notes 10-13
GQM 4.1

7
Tue
3/3
The Ring
z-component of angular momentum
Degeneracy
Comparison to Particle in a Box
Quantum States on a Ring
Worksheet: Quantum states on a Ring
Worksheet: Quantum states on a Ring
Worksheet: Quantum states on a Ring
Class Notes 14
G 9.3

8
Wed
3/4
Time Dependence on a Ring
Maple: The Ring
Worksheet: The Ring

9
Thu
3/5
The Rigid Rotor
Legendre's Equation
Change of Variables
Series Solutions
Legendre Polynomials
Rodrigues' formula
Graphs
Orthonormality
Legendre Polynomial Series
Maple: Guess
Worksheet: Guess
Maple: Finding Legendre Coefficients
Worksheet: Finding Legendre Coefficients
Class Notes 15-17
G 11.1
GQM 4.3

Class Notes 18-20

HW 3
Solutions

10
Fri
3/6
Legendre's Associated Equation
Legendre Functions
Spherical Harmonics
Orthonormality
GQM 4.1.2
GQM 4.3

HW 4
Solutions
11
Mon
3/9
Spherical Harmonics
Graphs
Maple: YLM's
Worksheet: YLM's
Symmetries, parity, degeneracy

12
Tue
3/10
Quantum States of the Rigid Rotor
Maple: Linear Combinations of YLMs
Worksheet: Linear Combinations of YLMs
Angular Momentum
Commutation Relations
Orbital Angular Momentum
Raising & lowering operators
Spin 1 revisited

GQM 4.3, G 11.2

13
Wed
3/11
Asymptotic Behavior
Laguerre polynomials
GQM 4.2, G 13.1

HW 5
Solutions

14
Thu
3/12
Hydrogen Atom Wave Functions
Symmetries, parity, degeneracy
Maple: Hydrogen Probablility Densities
Worksheet: Hydrogen Probability Densities
Applications
GQM 4.2, G 13.2

GQM 4.2.2

15
Fri
3/13
The Classical Limit
Review

HW 6
Solutions
Maple Sol

Legendre Polys