# Differential Equations of Quantum Mechanics

In general, the differential equations (DE) of quantum mechanics are special cases of eigenvalue problems. These pages offer an introduction to the mathematics of such problems for students of quantum chemistry or quantum physics. Several illustrative examples are given to show how the problems are solved using various methods. Exercises, some with solutions and some without, are presented to give students practice with solving typical quantum mechanics problems.

Parallel to the DE eigenvalue problems is an equivalent class of eigenvalue problems expressed in linear algebra (LA). Often the connection between a given DE eigenvalue problem and its LA equivalent is given.

## Map of the site

References | Introduction and Background...Quantum Mechanics Links |

Eigenvalue Problems from Classical
Physics...Mass on a Spring and Electrical Analog ...Simple Pendulum ...Sound Waves ...Vibrating String |
Orthonormal Basis Functions...Primary example: Fourier Series ...Example: Legendre Series ...Example: Hermite Polynomials |

Sturm-Liouville Theory...General S-L eigenvalue problem ...Example: Legendre's equation |
Numerical Integration Method for
Eigenvalues...Two Point Boundary Value Problems |

Quantum Mechanical Systems. I.
Analytical Solutions...Particle in a Box ...Particle in a Finite Well ...Simple Harmonic Oscillator ...Rigid Rotator in 3 dimensions ...Hydrogen Atom |
Quantum Mechanical Systems. II. Numerical
Solutions ...Particle in a Box, PIB ...PIB with central well ...PIB with spring |

Quantum Mechanical Systems. III. LA
solutions ...Variation Principle .. Particle in a Box (PIB) via polnomial Basis .. PIB with central well via Fourier Basis |
Time dependent Schroedinger Equation (under construction) see a preview |

Created or up-dated 08/03/99
by R.D. Poshusta

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