Quantum mechanics of a spinless particle in combined coulomb and harmonic oscillator potentials
In this dissertation the quantum mechanics of a spinless particle in a combined Coulomb and harmonic oscillator potential is discussed. The particular potential considered is a 2:1 anisotropic harmonic oscillator combined with a concentric Coulomb potential. These two potentials are the two most studied potentials in mathematical physics. It is shown that the combined potential gives a Schroedinger equation that separates in a parabolic coordinate system. The energy eigenfunctions for the pure oscillator is given by the product of polynomials in the parabolic coordinates and gaussians in these same coordinates. These eigenfunctions form a complete set. The discussion of the oscillator is closed with a short discussion of the algebraic aspects of the pure oscillator problem. When the Schroedinger equation for the combined potential is separated, two equations of identical form arise. The single equation obtained is one that has received very little attention in the past. The eigenvalues of the resulting pairs of equations are found numerically. The results for these eigenvalues are presented graphically, although a method for finding them explicitly is described. Once the eigenvalues are found, the wavefunctions may then be easily found.
- Research Organization:
- Case Western Reserve Univ., Cleveland, OH (USA)
- OSTI ID:
- 7014857
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
HARMONIC OSCILLATOR MODELS
COULOMB FIELD
QUANTUM MECHANICS
SCHROEDINGER EQUATION
COORDINATES
EIGENFUNCTIONS
EIGENVALUES
WAVE FUNCTIONS
DIFFERENTIAL EQUATIONS
ELECTRIC FIELDS
EQUATIONS
FUNCTIONS
MATHEMATICAL MODELS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
WAVE EQUATIONS
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics