Central Forces Spring 2018

Syllabus

Copies of the course notes can be found here:

Day Topic:
Subtopic
(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
Asymptotic Behavior
Hydrogenic atom wave functions
DM’s QM Chapter 8

25
Fri
6/8
Hydrogenic atoms
Hydrogen Atom II
Mathematica: Hydrogen Probablility Densities