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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 12.11-12
 
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
 
 
 
   
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
 
 
 
 
 
 
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
Math Bits
  Worksheet: Finding Legendre Coefficients
  Rodrigues' formula
  Graphs
  Orthonormality
 
 
 
 
 
 
 
       
15
Fri
5/25
The Rigid Rotor: Part I
Legendre's Associated Equation
  Legendre Functions
Spherical Harmonics
  Orthonormality
Symmetries, parity, degeneracy
 
 
 
 
 
HW 6
Solutions
   
16
Mon
5/28
MEMORIAL DAY
 
 
17
Tue
5/29
The Rigid Rotor: Part II
Legendre's Associated Equation
  Legendre Functions
 
 
  
18
Wed
5/30
Spherical Harmonics
  Orthonormality
Spherical Harmonics
  Graphs
  Mathematica: YLM's
Time Dependence
  Mathmetica: Linear Combinations of YLMs
 
 
 
 
 
HW 7
Solution to problem #1
Solution to problem #2
  
19
Thu
5/31
Angular Momentum I
  Angular Momentum I
 
 
20
Fri
6/1
Orbital Angular Momentum
  Raising & lowering operators
 
 
HW 8
Solutions
21
Mon
6/4
QUIZ #3
  QUIZ #3 & Solution
  Mathematica code for QUIZ #3
 
 
 
 
    
22
Tue
6/5
Angular Momentum I
  Angular Momentum I
 
 
23
Wed
6/6
Angular Momentum II
  Raising & lowering operators
 
 
 
HW 9
Solutions to problems #1, 2, 4 and 5
Solution to problem #3
24
Thu
6/7
Hydrogenic atoms
  Laguerre polynomials
  Radial Functions
  Asymptotic Behavior
  Hydrogenic atom wave functions
DM’s QM Chapter 8
 
 
 
 
     
25
Fri
6/8
Hydrogenic atoms
  Hydrogen Atom II
  Mathematica: Hydrogen Probablility Densities
  Mathematica: Radial Wavefunctions
DM’s QM Chapter 8
 
 
HW 10
Solutions
 

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