Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 46, Issue 41, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/46/41/415302
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Funding
- NBRPC [2012CB821305]
- NNSFC [11075223, 11147021]
- PhD Programs Foundation of Ministry of Education of China [20120171110022]
- NCETPC [NCET-10-0850]
- Hunan Provincial Natural Science Foundation [12JJ4010]
- 1000 Talents Program of China
- Australian Research Council
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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.
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