TY - JOUR
T1 - Exact solutions of the 1D Schrödinger equation with the Mathieu potential
AU - Sun, Guo Hua
AU - Chen, Chang Yuan
AU - Taud, Hind
AU - Yáñez-Márquez, C.
AU - Dong, Shi Hai
N1 - Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2020/7/2
Y1 - 2020/7/2
N2 - The exact solutions of the 1D Schrödinger equation with the Mathieu potential V(x)=a2sin2(bx)−ab(2c+1)cos(bx)+vb2 (a>0,b>0) are presented as a confluent Heun function HC(α,β,γ,δ,η;z). The eigenvalues are calculated precisely by solving the Wronskian determinant. The wave functions for the positive and negative parameter c, which correspond to two different potential wells with symmetric axis x=0 and x=π are plotted. It is found that the wave functions are shrunk to the origin for given values of the parameters a=1,b=1 and v=2 when the potential parameter |c| increases.
AB - The exact solutions of the 1D Schrödinger equation with the Mathieu potential V(x)=a2sin2(bx)−ab(2c+1)cos(bx)+vb2 (a>0,b>0) are presented as a confluent Heun function HC(α,β,γ,δ,η;z). The eigenvalues are calculated precisely by solving the Wronskian determinant. The wave functions for the positive and negative parameter c, which correspond to two different potential wells with symmetric axis x=0 and x=π are plotted. It is found that the wave functions are shrunk to the origin for given values of the parameters a=1,b=1 and v=2 when the potential parameter |c| increases.
KW - 1D Schrödinger equation
KW - Confluent Heun function
KW - Exact solutions
KW - Mathieu potential
KW - Wronskian determinant
UR - http://www.scopus.com/inward/record.url?scp=85083815075&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2020.126480
DO - 10.1016/j.physleta.2020.126480
M3 - Artículo
AN - SCOPUS:85083815075
SN - 0375-9601
VL - 384
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 19
M1 - 126480
ER -