Semi-exact Solutions of Konwent Potential

Qian Dong, Shi Shan Dong, Eduardo Hernández-Márquez, Ramón Silva-Ortigoza, Guo Hua Sun, Shi Hai Dong

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Abstract

© 2019 Chinese Physical Society and IOP Publishing Ltd. In this work we study the quantum system with the symmetric Konwent potential and show how to find its exact solutions. We find that the solutions are given by the confluent Heun function. The eigenvalues have to be calculated numerically because series expansion method does not work due to the variable z ≥ 1. The properties of the wave functions depending on the potential parameter A are illustrated for given potential parameters V 0 and a. The wave functions are shrunk towards the origin with the increasing |A|. In particular, the amplitude of wave function of the second excited state moves towards the origin when the positive parameter A decreases. We notice that the energy levels i increase with the increasing potential parameter |A| ≥ 1, but the variation of the energy levels becomes complicated for |A| ∈ (0, 1), which possesses a double well. It is seen that the energy levels i increase with |A| for the parameter interval A ∈ (-1, 0), while they decrease with |A| for the parameter interval A ∈ (0, 1).
Original languageAmerican English
Pages (from-to)231-236
Number of pages207
JournalCommunications in Theoretical Physics
DOIs
StatePublished - 1 Feb 2019

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energy levels
wave functions
intervals
series expansion
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title = "Semi-exact Solutions of Konwent Potential",
abstract = "{\circledC} 2019 Chinese Physical Society and IOP Publishing Ltd. In this work we study the quantum system with the symmetric Konwent potential and show how to find its exact solutions. We find that the solutions are given by the confluent Heun function. The eigenvalues have to be calculated numerically because series expansion method does not work due to the variable z ≥ 1. The properties of the wave functions depending on the potential parameter A are illustrated for given potential parameters V 0 and a. The wave functions are shrunk towards the origin with the increasing |A|. In particular, the amplitude of wave function of the second excited state moves towards the origin when the positive parameter A decreases. We notice that the energy levels i increase with the increasing potential parameter |A| ≥ 1, but the variation of the energy levels becomes complicated for |A| ∈ (0, 1), which possesses a double well. It is seen that the energy levels i increase with |A| for the parameter interval A ∈ (-1, 0), while they decrease with |A| for the parameter interval A ∈ (0, 1).",
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Semi-exact Solutions of Konwent Potential. / Dong, Qian; Dong, Shi Shan; Hernández-Márquez, Eduardo; Silva-Ortigoza, Ramón; Sun, Guo Hua; Dong, Shi Hai.

In: Communications in Theoretical Physics, 01.02.2019, p. 231-236.

Research output: Contribution to journalArticle

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AU - Dong, Qian

AU - Dong, Shi Shan

AU - Hernández-Márquez, Eduardo

AU - Silva-Ortigoza, Ramón

AU - Sun, Guo Hua

AU - Dong, Shi Hai

PY - 2019/2/1

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N2 - © 2019 Chinese Physical Society and IOP Publishing Ltd. In this work we study the quantum system with the symmetric Konwent potential and show how to find its exact solutions. We find that the solutions are given by the confluent Heun function. The eigenvalues have to be calculated numerically because series expansion method does not work due to the variable z ≥ 1. The properties of the wave functions depending on the potential parameter A are illustrated for given potential parameters V 0 and a. The wave functions are shrunk towards the origin with the increasing |A|. In particular, the amplitude of wave function of the second excited state moves towards the origin when the positive parameter A decreases. We notice that the energy levels i increase with the increasing potential parameter |A| ≥ 1, but the variation of the energy levels becomes complicated for |A| ∈ (0, 1), which possesses a double well. It is seen that the energy levels i increase with |A| for the parameter interval A ∈ (-1, 0), while they decrease with |A| for the parameter interval A ∈ (0, 1).

AB - © 2019 Chinese Physical Society and IOP Publishing Ltd. In this work we study the quantum system with the symmetric Konwent potential and show how to find its exact solutions. We find that the solutions are given by the confluent Heun function. The eigenvalues have to be calculated numerically because series expansion method does not work due to the variable z ≥ 1. The properties of the wave functions depending on the potential parameter A are illustrated for given potential parameters V 0 and a. The wave functions are shrunk towards the origin with the increasing |A|. In particular, the amplitude of wave function of the second excited state moves towards the origin when the positive parameter A decreases. We notice that the energy levels i increase with the increasing potential parameter |A| ≥ 1, but the variation of the energy levels becomes complicated for |A| ∈ (0, 1), which possesses a double well. It is seen that the energy levels i increase with |A| for the parameter interval A ∈ (-1, 0), while they decrease with |A| for the parameter interval A ∈ (0, 1).

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