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Quantum Engineering Year 0: Mathematical Foundations Month 8Day 200

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Year 0·Month 8·Week 1

Day 200: Boundary Value Problems

Day 200 of 2,016~10 min read

Learning Objectives

•Apply separation of variables to Laplace's equation in Cartesian coordinates
•Solve boundary value problems with Dirichlet and Neumann conditions
•Apply separation of variables in spherical coordinates
•Recognize Legendre polynomials as angular solutions
•Connect to the angular part of the hydrogen atom wave function
•Implement numerical solutions using finite differences

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1 Separation of Variables The Key Technique 2 Solutions in a Rectangular Box 3 Laplaces Equation in Spherical Coordinates 4 Spherical Harmonics 5 Azimuthally Symmetric Problems 6 Uniqueness Theorems Quantum Mechanics Connection Hydrogen Atom The Same Equation The Quantum Numbers Radial Schrdinger vs Laplace

Day 199Day 200 of 2,016Day 201