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2013 | 11 | 3 | 279-290
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
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.
Wydawca

Czasopismo
Rocznik
Tom
11
Numer
3
Strony
279-290
Opis fizyczny
Daty
wydano
2013-03-01
online
2013-03-28
Twórcy
  • Department of Mathematics and Statistics, University of Prince Edward Island, 550 University Avenue, Charlottetown, PEI, Canada, C1A 4P3, dbrandon@upei.ca
autor
  • 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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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-013-0179-3
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