Orthogonal Polynomials in Physics

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Casting ODEs into Sturm-Liouville form

Explores casting ODEs into self-adjoint form and the role of boundary conditions in ensuring self-adjointness.

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Interlacing Polynomials

Explores interlacing polynomials, real rooted theorems, and pseudo-probabilistic methods in polynomial analysis.

Quantum Harmonic Oscillator

Explores the quantum harmonic oscillator, creation and annihilation operators, energy levels, and wave functions.

Quantum Physics: Orbital Angular Momentum

Delves into orbital angular momentum in quantum physics, emphasizing spherical harmonics' significance and normalization conditions.

Spherical Harmonics

Explores spherical harmonics, discussing their mathematical properties and significance in quantum mechanics.

Taylor Polynomials: Special Cases

Explores Taylor polynomials, odd orders, simplification, residues, and special cases of zero polynomials.

Quantum Wells: Coupled Quantum States and Energy Levels

Covers quantum wells, coupled states, energy levels, and the implications for molecular formation.

Polynomials: Definitions and Operations

Covers the definition and operations of polynomials, including addition and multiplication, degree, coefficients, and their role in algebraic systems.

Legendre Functions of 2nd Kind & Spherical Harmonics

Explores Legendre functions of the second kind and spherical harmonics properties and relationships.