Resumen
We find that the analytical solutions to quantum system with a quartic potential V (x) = ax2 + bx4 (arbitrary a and b > 0 are real numbers) are given by the triconfluent Heun functions HT(α,β,γ; z). The properties of the wave functions, which are strongly relevant for the potential parameters a and b, are illustrated. It is shown that the wave functions are shrunk to the origin for a given b when the potential parameter a increases, while the wave peak of wave functions is concaved to the origin when the negative potential parameter |a| increases or parameter b decreases for a given negative potential parameter a. The minimum value of the double well case (a < 0) is given by Vmin = -a2/(4b) at x = ±|a|/2b.
Idioma original | Inglés |
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Número de artículo | 1950208 |
Publicación | Modern Physics Letters A |
Volumen | 34 |
N.º | 26 |
DOI | |
Estado | Publicada - 30 ago. 2019 |