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Central Forces
 
Spring 2018

Syllabus

Tentative: Check Often For Updates

Copies of the course notes can be found here:

     Classical Mechanics

     Quantum (Separation of Variables)

     Quantum (The Ring and the Sphere)

Day Topic:
  Subtopic
Reading
  (Main, Alternate,  Deep)
Due Dates
1
Mon
5/7
Math Bits
  Series Solutions
Boas 12.1-2
Boas 12.11-12
 
2
Tue
5/8
Math Bits
  Change of Variables
Boas 8.4, 8.7
 
3
Wed
5/9
Introduction to Central Forces
Systems of Particles
  Center of Mass
  Survivor Hockey Ring
Two-body Problems
  Newton’s Second Law for Center of Mass
  Newton’s Second Law for Reduced Mass
  Central Forces
T 1.1-1.4
 
T 3.3, 10.1
 
 
 
T 8.2
T 8.1
HW 1
Solutions
      
4
Thu
5/10
Classical Angular Momentum
  Torque
  Conservation of Angular Momentum
  Kepler's Second Law
 
 
T 3.1, 3.4-3.5, 10.1
 
    
5
Fri
5/11
Velocity and Acceleration
  Worksheet: Vel. & Acc.-Polar Coords.
 
 
 
 HW 2
Solutions
6
Mon
5/14
QUIZ
  Quiz #1
  Quiz #1 Solution
Review
  Review of Week 01
Equations of Motion: F=ma
Orbit Shapes
Inverse Square Forces
  Kepler's first law
 
 
 
T 8.3
 
 
      
7
Tue
5/15
Polar Graphs
Circles, Ellipses, Hyperbolas
  Mathematica: Conic Sections
Equations of Motion: E=T+U
  Class notes on E = T + U
Effective Potentials
  Mathematica: Effective Potentials
 
 
 
T 8.4
    
8
Wed
5/16
Inverse Square Forces
  Orbits
  Mathematica: Orbits
Other Force Laws
Orbits Summary
Recap
T 8.5-8.7
 
 
 
 
HW 3
Solutions
   
9
Thu
5/17
Schroedinger's Eqn.
  Spherical Symmetry
  Separation of Variables
  Ĥ, L^2, Lz
 
GQM 4.1
 
   
10
Fri
5/18
Particle on a ring (aka 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
G 9.3
 
 
 
 
 
HW 4
Solutions
    
11
Mon
5/21
QUIZ
Time Dependence on a Ring
  Mathematica: The Ring
  Worksheet: The Ring
 
 
 
 
    
12
Tue
5/22
Math Bits
  Sturm-Liouville
  Particle in a 2-D Box
 
 
  
13
Wed
5/23
Math Bits
  Boundary Conditions
 
 
HW 5
Solutions
14
Thu
5/24
Math Bits
  Legendre Polynomial Series
  Mathematica: Guess
  Worksheet: Guess
  Mathematica: Finding Legendre Coefficients
Math Bits
  Worksheet: Finding Legendre Coefficients
  Rodrigues' formula
  Graphs
  Orthonormality
 
 
 
 
 
 
 
 
        
15
Fri
5/25
The Rigid Rotor
Legendre's Associated Equation
  Legendre Functions
Spherical Harmonics
  Orthonormality
Spherical Harmonics
  Graphs
  Mathematica: YLM's
  Worksheet: YLM's
Symmetries, parity, degeneracy
G 11.1
GQM 4.3
GQM 4.1.2
GQM 4.3
 
 
 
 
 
HW 6
Solutions
      
16
Mon
5/28
MEMORIAL DAY
 
 
17
Tue
5/29
Quantum States of the Rigid Rotor
  Maple: Linear Combinations of YLMs
  Worksheet: Linear Combinations of YLMs
 
 
  
18
Wed
5/30
Time Dependence
Angular Momentum
  Commutation Relations
 
 
HW 7
Solutions
19
Thu
5/31
Orbital Angular Momentum
  Raising & lowering operators
  Spin 1 revisited
GQM 4.3, G 11.2
 
  
20
Fri
6/1
The Radial Equation
  Radial Functions
  Asymptotic Behavior
  Laguerre polynomials
  Mathematica: Radial Wavefunctions
  Worksheet: Radial Wavefunctions
 
GQM 4.2, G 13.1
 
 
 
 
HW 8
Solutions
    
21
Mon
6/4
QUIZ
Hydrogen Atom Wave Functions
  Symmetries, parity, degeneracy
  Mathematica: Hydrogen Probablility Densities
  Worksheet: Hydrogen Probability Densities
 
GQM 4.2, G 13.2
 
 
    
22
Tue
6/5
The Classical Limit
 
 
  
23
Wed
6/6
Applications
GQM 4.2.2
 
HW 9
Solutions
24
Thu
6/7
Scattering
T 14.1-14.6
 
25
Fri
6/8
Review
 
 
HW 10
Solutions

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