| Resumen |
The exact solutions to a one-dimensional harmonic oscillator plus a non-polynomial interaction ax(2) + bx(2)/(1 + cx(2)) (a > 0, c > 0) are given by the confluent Heun functions H-c(alpha, beta, gamma, delta, eta;z). The minimum value of the potential well is calculated as V-min(x) = -(a+vertical bar b vertical bar-2 root a vertical bar b vertical bar)/c at x = +/-[(root vertical bar b/a-1)/c](1/2) (vertical bar b vertical bar>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 vertical bar b vertical bar is increased. |
