TY - JOUR
T1 - Analytical eigenstates for the quantum Rabi model
AU - Zhong, Honghua
AU - Xie, Qiongtao
AU - Batchelor, Murray T.
AU - Lee, Chaohong
PY - 2013/10/18
Y1 - 2013/10/18
N2 - We develop a method to find analytical solutions for the eigenstates of the quantum Rabi model. These include symmetric, anti-symmetric and asymmetric analytic solutions given in terms of the confluent Heun functions. Both regular and exceptional solutions are given in a unified form. In addition, the analytic conditions for determining the energy spectrum are obtained. Our results show that conditions proposed by Braak (2011 Phys. Rev. Lett. 107 100401) are a type of sufficiency condition for determining the regular solutions. The well-known Judd isolated exact solutions appear naturally as truncations of the confluent Heun functions.
AB - We develop a method to find analytical solutions for the eigenstates of the quantum Rabi model. These include symmetric, anti-symmetric and asymmetric analytic solutions given in terms of the confluent Heun functions. Both regular and exceptional solutions are given in a unified form. In addition, the analytic conditions for determining the energy spectrum are obtained. Our results show that conditions proposed by Braak (2011 Phys. Rev. Lett. 107 100401) are a type of sufficiency condition for determining the regular solutions. The well-known Judd isolated exact solutions appear naturally as truncations of the confluent Heun functions.
UR - http://www.scopus.com/inward/record.url?scp=84885118190&partnerID=8YFLogxK
U2 - 10.1088/1751-8113/46/41/415302
DO - 10.1088/1751-8113/46/41/415302
M3 - Article
SN - 1751-8113
VL - 46
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 41
M1 - 415302
ER -