Mathematical Methods
3 Operators, Eigenvectors and Eigenvalues
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Notes
1
Introduction and Prerequisites
2
Linear vector spaces
3
Operators, Eigenvectors and Eigenvalues
4
Green functions
5
Variational calculus
A
Contour Integration
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Chapter 3
Operators, Eigenvectors and Eigenvalues
3.1
Linear operators
3.1.1
Domain, Codomain and Range
3.1.2
Matrix representations of linear operators
3.1.3
Adjoint operator and hermitian operators
3.2
Eigenvalue equations
3.2.1
Problems
3.3
Sturm-Liouville equations
3.3.1
How to bring an equation to Sturm-Liouville form
3.3.2
A useful result
3.3.3
Hermitian Sturm Liouville operators
3.3.4
Second solutions, singularities
3.3.5
Eigenvectors and eigenvalues
3.4
Series solutions and orthogonal polynomials
3.4.1
The quantum-mechanical oscillator and Hermite polynomials
3.4.2
Legendre polynomials
3.4.3
Bessel functions and the circular drum
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