TY - JOUR

T1 - Exact solutions of the harmonic oscillator plus non-polynomial interaction

T2 - Exact solutions for HO plus non polynom

AU - Dong, Qian

AU - Iván García Hernández, H.

AU - Sun, Guo Hua

AU - Toutounji, Mohamad

AU - Dong, Shi Hai

N1 - Funding Information:
Data accessibility. This article does not contain any additional data. Authors’ contributions. All authors contributed equally to the writing and revision of the manuscript. Competing interests. We declare we have no competing interests. Funding. This work is supported by project 20200981-SIP-IPN, COFAA-IPN, Mexico and partially by the CONACYT project under grant no. 288856-CB-2016. Acknowledgements. We would like to thank the kind referees for making invaluable and positive suggestions, which have improved the manuscript greatly.
Publisher Copyright:
© 2020 The Author(s).

PY - 2020/9/1

Y1 - 2020/9/1

N2 - The exact solutions to a one-dimensional harmonic oscillator plus a non-polynomial interaction a x 2 + b x 2 /(1 + c x 2) (a > 0, c > 0) are given by the confluent Heun functions H c (a, ß, ?, d, ?;z). The minimum value of the potential well is calculated as Vmin(x)=-(a+|b|-2a |b|)/c at x=±[(|b|/a-1)/c]1/2 (|b| > a) for the double-well case (b < 0). We illustrate the wave functions through varying the potential parameters a, b, c and show that they are pulled back to the origin when the potential parameter b increases for given values of a and c. However, we find that the wave peaks are concave to the origin as the parameter |b| is increased.

AB - The exact solutions to a one-dimensional harmonic oscillator plus a non-polynomial interaction a x 2 + b x 2 /(1 + c x 2) (a > 0, c > 0) are given by the confluent Heun functions H c (a, ß, ?, d, ?;z). The minimum value of the potential well is calculated as Vmin(x)=-(a+|b|-2a |b|)/c at x=±[(|b|/a-1)/c]1/2 (|b| > a) for the double-well case (b < 0). We illustrate the wave functions through varying the potential parameters a, b, c and show that they are pulled back to the origin when the potential parameter b increases for given values of a and c. However, we find that the wave peaks are concave to the origin as the parameter |b| is increased.

KW - confluent Heun function

KW - exact solutions

KW - non-polynomial oscillator

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U2 - 10.1098/rspa.2020.0050

DO - 10.1098/rspa.2020.0050

M3 - Article

AN - SCOPUS:85093077893

SN - 0950-1207

VL - 476

JO - PROC. R. SOC. - A.

JF - PROC. R. SOC. - A.

IS - 2241

M1 - 20200050

ER -