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Number of results

Journal

2013 | 11 | 3 | 279-290

Article title

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

Content

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Languages of publication

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
author
  • Department of Mathematics and Statistics, University of Prince Edward Island, 550 University Avenue, Charlottetown, PEI, Canada, C1A 4P3

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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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