Dong Qian, Iván García Hernández H, Sun Guo-Hua, Toutounji Mohamad, Dong Shi-Hai
CIC, Instituto Politécnico Nacional, Ciudad de Mexico 07700, Mexico.
Catedrática CONACYT, CIC, Instituto Politécnico Nacional, Ciudad de Mexico 07700, Mexico.
Proc Math Phys Eng Sci. 2020 Sep;476(2241):20200050. doi: 10.1098/rspa.2020.0050. Epub 2020 Sep 23.
The exact solutions to a one-dimensional harmonic oscillator plus a non-polynomial interaction + /(1 + ) ( > 0, > 0) are given by the confluent Heun functions (, , , , ;). The minimum value of the potential well is calculated as at (|| > ) for the double-well case ( < 0). We illustrate the wave functions through varying the potential parameters , , and show that they are pulled back to the origin when the potential parameter increases for given values of and . However, we find that the wave peaks are concave to the origin as the parameter || is increased.
一维谐振子加上非多项式相互作用 + /(1 + ) ( > 0, > 0)的精确解由合流超几何函数 (, , , , ;)给出。对于双阱情形( < 0)，势阱的最小值在(|| > )处计算为 。我们通过改变势参数, , 来说明波函数，并表明对于给定的 和 值，当势参数 增加时，它们会被拉回到原点。然而，我们发现随着参数||的增加，波峰向原点凹陷。
