TY - JOUR
T1 - Exact solutions of a nonpolynomial oscillator related to isotonic oscillator
AU - Dong, Qian
AU - Sun, Guo Hua
AU - Saad, N.
AU - Dong, Shi Hai
N1 - Publisher Copyright:
© 2019, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/11/1
Y1 - 2019/11/1
N2 - We find that the analytical solutions to a quantum system with a nonpolynomial oscillator potential related to isotonic oscillator are given by the confluent Heun functions Hc(α, β, γ, δ, η; z). The properties of the wave functions, which are strongly relevant for the potential parameters a and g, are illustrated. It is shown that the wave functions are shrunk to the origin for a given a when the potential parameter g increases, while the wave peak of wave functions is concaved to the origin when the negative potential parameter | g| increases. Moreover, the wave peaks of the even wave functions become sharper when the potential parameter a< 1 decreases, but they become flat when the potential parameter a> 1 increases. When the minimum value Vmin= - g/ a2 tends to zero, this nonpolynomial oscillator reduces to a harmonic oscillator.
AB - We find that the analytical solutions to a quantum system with a nonpolynomial oscillator potential related to isotonic oscillator are given by the confluent Heun functions Hc(α, β, γ, δ, η; z). The properties of the wave functions, which are strongly relevant for the potential parameters a and g, are illustrated. It is shown that the wave functions are shrunk to the origin for a given a when the potential parameter g increases, while the wave peak of wave functions is concaved to the origin when the negative potential parameter | g| increases. Moreover, the wave peaks of the even wave functions become sharper when the potential parameter a< 1 decreases, but they become flat when the potential parameter a> 1 increases. When the minimum value Vmin= - g/ a2 tends to zero, this nonpolynomial oscillator reduces to a harmonic oscillator.
UR - http://www.scopus.com/inward/record.url?scp=85075087812&partnerID=8YFLogxK
U2 - 10.1140/epjp/i2019-12980-7
DO - 10.1140/epjp/i2019-12980-7
M3 - Artículo
AN - SCOPUS:85075087812
SN - 2190-5444
VL - 134
JO - European Physical Journal Plus
JF - European Physical Journal Plus
IS - 11
M1 - 562
ER -