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

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.