An eigenfunction expansion for the Schrodinger equation with arbitrary non-central potentials

Date

2002-11-01

Author

Taşeli, Hasan
Uğur, Ömür

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An eigenfunction expansion for the Schrodinger equation for a particle moving in an arbitrary non-central potential in the cylindrical polar coordinates is introduced, which reduces the partial differential equation to a system of coupled differential equations in the radial variable r. It is proved that such an orthogonal expansion of the wavefunction into the complete set of Chebyshev polynomials is uniformly convergent on any domain of (r, theta). As a benchmark application, the bound states calculations of the quartic oscillator show that both analytical and numerical implementations of the present method are quite satisfactory.

Subject Keywords

Two-dimensional Schrodinger equation, Eigenfunction expansion, Eigenvalue problems

URI

https://hdl.handle.net/11511/32558

Journal

JOURNAL OF MATHEMATICAL CHEMISTRY

DOI

https://doi.org/10.1023/a:1022949421571

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

H. Taşeli and Ö. Uğur, “An eigenfunction expansion for the Schrodinger equation with arbitrary non-central potentials,” JOURNAL OF MATHEMATICAL CHEMISTRY, pp. 323–338, 2002, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32558.