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Journal
2013 | 11 | 3 | 279-290
Article title

Exact and approximate solutions to Schrödinger’s equation with decatic potentials

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EN
Abstracts
EN
The one-dimensional Schrödinger’s equation is analysed with regard to the existence of exact solutions for decatic polynomial potentials. Under certain conditions on the potential’s parameters, we show that the decatic polynomial potential V (x) = ax
10 + bx
8 + cx
6 + dx
4 + ex
2, a > 0 is exactly solvable. By examining the polynomial solutions of certain linear differential equations with polynomial coefficients, the necessary and sufficient conditions for corresponding energy-dependent polynomial solutions are given in detail. It is also shown that these polynomials satisfy a four-term recurrence relation, whose real roots are the exact energy eigenvalues. Further, it is shown that these polynomials generate the eigenfunction solutions of the corresponding Schrödinger equation. Further analysis for arbitrary values of the potential parameters using the asymptotic iteration method is also presented.
Publisher

Journal
Year
Volume
11
Issue
3
Pages
279-290
Physical description
Dates
published
1 - 3 - 2013
online
28 - 3 - 2013
Contributors
author
  • Department of Mathematics and Statistics, University of Prince Edward Island, 550 University Avenue, Charlottetown, PEI, Canada, C1A 4P3, dbrandon@upei.ca
author
  • Department of Mathematics and Statistics, University of Prince Edward Island, 550 University Avenue, Charlottetown, PEI, Canada, C1A 4P3, nsaad@upei.ca
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Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-013-0179-3
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