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 - 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 - 1364-5021

VL - 476

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

IS - 2241

M1 - 20200050

ER -