Quantum mechanical computation of billiard systems with arbitrary shapes

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2003

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Erhan, İnci

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An expansion method for the stationary Schrodinger equation of a particle moving freely in an arbitrary axisymmeric three dimensional region defined by an analytic function is introduced. The region is transformed into the unit ball by means of coordinate substitution. As a result the Schrodinger equation is considerably changed. The wavefunction is expanded into a series of spherical harmonics, thus, reducing the transformed partial differential equation to an infinite system of coupled ordinary differential equations. A Fourier-Bessel expansion of the solution vector in terms of Bessel functions with real orders is employed, resulting in a generalized matrix eigenvalue problem. The method is applied to two particular examples. The first example is a prolate spheroidal billiard which is also treated by using an alternative method. The numerical results obtained by using both the methods are compared. The second exampleis a billiard family depending on a parameter. Numerical results concerning the second example include the statistical analysis of the eigenvalu

Subject Keywords

Schrödinger equation, Eigenfunction expansions, Eigenvalues

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http://etd.lib.metu.edu.tr/upload/2/1104082/index.pdf
https://hdl.handle.net/11511/13737

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Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

İ. Erhan, “Quantum mechanical computation of billiard systems with arbitrary shapes,” Ph.D. - Doctoral Program, Middle East Technical University, 2003.