TY - JOUR
T1 - Semi-exact Solutions of Konwent Potential
AU - Dong, Qian
AU - Dong, Shi Shan
AU - Hernández-Márquez, Eduardo
AU - Silva-Ortigoza, Ramón
AU - Sun, Guo Hua
AU - Dong, Shi Hai
N1 - Publisher Copyright:
© 2019 Chinese Physical Society and IOP Publishing Ltd.
PY - 2019/2/1
Y1 - 2019/2/1
N2 - In this work we study the quantum system with the symmetric Konwent potential and show how to find its exact solutions. We find that the solutions are given by the confluent Heun function. The eigenvalues have to be calculated numerically because series expansion method does not work due to the variable z ≥ 1. The properties of the wave functions depending on the potential parameter A are illustrated for given potential parameters V 0 and a. The wave functions are shrunk towards the origin with the increasing |A|. In particular, the amplitude of wave function of the second excited state moves towards the origin when the positive parameter A decreases. We notice that the energy levels i increase with the increasing potential parameter |A| ≥ 1, but the variation of the energy levels becomes complicated for |A| ∈ (0, 1), which possesses a double well. It is seen that the energy levels i increase with |A| for the parameter interval A ∈ (-1, 0), while they decrease with |A| for the parameter interval A ∈ (0, 1).
AB - In this work we study the quantum system with the symmetric Konwent potential and show how to find its exact solutions. We find that the solutions are given by the confluent Heun function. The eigenvalues have to be calculated numerically because series expansion method does not work due to the variable z ≥ 1. The properties of the wave functions depending on the potential parameter A are illustrated for given potential parameters V 0 and a. The wave functions are shrunk towards the origin with the increasing |A|. In particular, the amplitude of wave function of the second excited state moves towards the origin when the positive parameter A decreases. We notice that the energy levels i increase with the increasing potential parameter |A| ≥ 1, but the variation of the energy levels becomes complicated for |A| ∈ (0, 1), which possesses a double well. It is seen that the energy levels i increase with |A| for the parameter interval A ∈ (-1, 0), while they decrease with |A| for the parameter interval A ∈ (0, 1).
KW - Konwent potential
KW - confluent Heun function
KW - double well potential
KW - exact solution
UR - http://www.scopus.com/inward/record.url?scp=85062990663&partnerID=8YFLogxK
U2 - 10.1088/0253-6102/71/2/231
DO - 10.1088/0253-6102/71/2/231
M3 - Artículo
SN - 0253-6102
VL - 71
SP - 231
EP - 236
JO - Communications in Theoretical Physics
JF - Communications in Theoretical Physics
IS - 2
M1 - 231
ER -