Copies of the course notes can be found here:
Quantum (Separation of Variables)
Quantum (The Ring and the Sphere)
Separation of Variables: The diffusion equation
Day | Topic: Subtopic |
Reading (Main, Alternate, Deep) |
Due Dates |
---|---|---|---|
1 Mon 5/6 |
Math Bits Series Solutions |
Class Notes 22 | |
2 Tue 5/7 |
Math Bits Series Solutions |
| |
3 Wed 5/8 |
Two-body Problems Center of Mass Survivor Hockey Ring Newton’s Second Law for Center of Mass |
Class Notes 1-3 | |
4 Thu 5/9 |
Two-body Problems Newton’s Second Law for Reduced Mass Motion of the Reduced Mass µ: Central Forces Central Forces Torque on µ Conservation of angular momentum for µ Worksheet: Velocity and Acceleration in Polar Coordinates. Worksheet answer |
T 8.2 T 8.1 T 3.1, 3.4-3.5, 10.1 |
Homework #1 Solutions |
5 Fri 5/10 |
Motion of the Reduced Mass µ: Central Forces Kepler's second law of planetary motion Equations of motion in polar coordinates Conservation of angular momentum Conservation of energy |
|
Homework #2 Solutions |
6 Mon 5/13 |
QUIZ Orbit Shapes of µ: Inverse Square Forces Kepler's first law of planetary motion |
| |
7 Tue 5/14 |
Potentials Polar Graphs Circles, Ellipses, Hyperbolas Mathematica: Conic Sections |
| |
8 Wed 5/15 |
Equations of Motion: E=T+U Effective Potentials Mathematica: Effective Potentials |
T 8.4 |
Homework #3 Solutions |
9 Thu 5/16 |
Inverse Square Forces Kepler's third law of planetary motion Schroedinger's Eqn. Spherical Symmetry |
Class Notes 10-13 | |
10 Fri 5/17 |
Schroedinger's Eqn. Important relations in spherical coordinates |
|
Homework #4 Solutions |
11 Mon 5/20 |
The Ring z-component of angular momentum energy degeneracy |
Class Notes 17-18 | |
12 Tue 5/21 |
Quantum States on a Ring Worksheet: Quantum states on a Ring Worksheet: Quantum states on a Ring Worksheet: Quantum states on a Ring |
| |
13 Wed 5/22 |
Time Dependence on a Ring Time dependence of a particle on the ring |
Class Notes 19 |
Homework #5 Solutions |
14 Thu 5/23 |
More Time Dependence Math Bits PDEs in Physics PDE Classification PDE Theorems Start Rigid Rotor Start Particle in 2-D Box |
LinAlg 9.1 LinAlg 9.2 LinAlg 9.3 Class Notes 20 | |
15 Fri 5/24 |
Math Bits Separation of Variables Change of Variables |
LinAlg 9.4 Class Notes 15-16 Class Notes 21 |
Homework #6 Solutions |
16 Mon 5/27 |
MEMORIAL DAY |
| |
17 Tue 5/28 |
Math Bits Boundary Conditions Legendre Polynomials Legendre Polynomial Series Sturm-Liouville Theory Mathematica: Guess Worksheet: Guess Mathematica: Finding Legendre Coefficients Worksheet: Finding Legendre Coefficients Rodrigues' formula Graphs Orthonormality |
Class Notes 23 Class Notes 24 LinAlg 9.5 Class Notes 18-20 | |
18 Wed 5/29 |
Quiz Math Bits Associate Legendre Functions |
GQM 4.1.2 GQM 4.3 Class Notes 25 |
Homework #7 Solutions |
19 Thu 5/30 |
Spherical Harmonics Orthonormality Spherical Harmonics Graphs Mathematica: YLM's Worksheet: YLM's Symmetries, parity, degeneracy Quantum States of the Rigid Rotor Linear Combinations of YLMs Worksheet: Linear Combinations of YLMs |
Class Notes 26 | |
20 Fri 5/31 |
Quantum States of the Rigid Rotor Linear Combinations of YLMs Worksheet: Linear Combinations of YLMs |
|
Homework #8 Solutions Mathematica code for prob #1 |
21 Mon 6/3 |
QUIZ Hydrogen Atom Wave Functions I The Radial Equation |
| |
22 Tue 6/4 |
Hydrogen Atom Wave Functions II Radial Functions Asymptotic Behavior |
GQM 4.2, G 13.1 | |
23 Wed 6/5 |
Hydrogen Atom Wave Functions III Laguerre polynomials Hydrogen Atom Wave Functions Symmetries, parity, degeneracy |
GQM 4.2, G 13.2 |
Homework #9 Solutions |
24 Thu 6/6 |
Hydrogen Atom Wave Functions IV Mathematica: Radial Wavefunctions Mathematica: Hydrogen Probablility Densities |
| |
25 Fri 6/7 |
Theory of Angular Momentum Commutation Relations Raising & lowering operators |
GQM 4.3, G 11.2 |
Homework #10 Solutions |
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