The influence of the boundedness of polynomial potentials on the spectrum of the Schrödinger equation

Taşeli, Hasan

doi:10.1016/0021-9991(92)90002-g

Cited by 17 publications

(10 citation statements)

References 20 publications

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“…In fact, we have observed thatL depends only on the number of basis functions N not on the south after energy levels. This is also true for the case of Dirichlet boundary condition [25,26,27,28]. In principle, we need to use more basis functions to obtain the same accuracy for the higher energy levels.…”

Section: Resultsmentioning

confidence: 99%

“…as basis set, in order to solve double-well potential and some other anharmonic symmetric oscillators [25,26,27,28]. They have shown that the trigonometric functions are a suitable basis-set in variational calculations in order to obtain highly accurate results.…”

Section: Introductionmentioning

confidence: 99%

“…They have shown that the trigonometric functions are a suitable basis-set in variational calculations in order to obtain highly accurate results. Moreover, the model is simple, fast-convergent, efficient and works for different kind of potentials [25,26,27,28].…”

Section: Introductionmentioning

confidence: 99%

“…[25,26,27,28], it was shown by numerical results that the eigenfunctions which obey Dirichlet boundary condition…”

Section: Introductionmentioning

confidence: 99%

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Accurate energy spectrum for double-well potential: periodic basis

2010

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We present a variational study of employing the trigonometric basis functions satisfying periodic boundary condition for the accurate calculation of eigenvalues and eigenfunctions of quartic double-well oscillators. Contrary to usual Dirichlet boundary condition, imposing periodic boundary condition on the basis functions results in the existence of an inflection point with vanishing curvature in the graph of the energy versus the domain of the variable. We show that this boundary condition results in a higher accuracy in comparison to Dirichlet boundary condition. This is due to the fact that the periodic basis functions are not necessarily forced to vanish at the boundaries and can properly fit themselves to the exact solutions.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…[25,26,27,28], it was shown by numerical results that the eigenfunctions which obey Dirichlet boundary condition…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Accurate energy spectrum for double-well potential: periodic basis

2010

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“…One can further argue that analytic (polynomial) solutions provide a deeper quantitative insight into the physical model under investigation and in many cases makes the conceptual understanding of physics straightforward and sometimes intuitive [6,24,25,45,59]. Moreover, these solutions (if they are available) are valuable tools for checking and improving numerical methods introduced for solving complicated physical systems [6,54].…”

Section: Introductionmentioning

confidence: 99%

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

Brandon

Saad

2013

Open Physics

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Abstract: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 ( ) = 10 + 8 + 6 + 4 + 2 , > 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. PACS

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Eigenvalues of the two-dimensional Schr�dinger equation with nonseparable potentials

Taşeli

Eid

1996

Int. J. Quantum Chem.

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mThe energy eigenvalues of coupled oscillators in two dimensions with quartic and sextic couplings have been calculated to a high accuracy. For this purpose, unbounded domain of the wave function has been truncated and various combination of trigonometric functions are employed as the basis sets in a Rayleigh-Ritz variational method. The method is applicable to the multiwell oscillators as well. 0 1996 John Wiley & Sons, Inc.

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The influence of the boundedness of polynomial potentials on the spectrum of the Schrödinger equation

Cited by 17 publications

References 20 publications

Accurate energy spectrum for double-well potential: periodic basis

Accurate energy spectrum for double-well potential: periodic basis

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

Eigenvalues of the two-dimensional Schr�dinger equation with nonseparable potentials

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