Integrable Quantum Systems  

In General > s.a. coherent states; integrable classical systems; non-commutative theories; special potentials [exactly solvable, etc].
* Idea: Quantum systems for which the energy spectrum can be explicitly computed.
* Energy eigenvalues: The energies of the tori whose actions in the semiclassical limit are of the form (n + k/8) h, with n arbitrary and k some fixed integer [KAM theory; & Einstein; Brillouin; Keller; Maslov].
@ General references: Kundu ht/96, ht/97-conf [rev]; Prykarpatsky & Mykytiuk 98 [geometric]; Hikami & Wadati JMP(03); Clemente-Gallardo & Marmo IJGMP(09)-a0808 [towards a definition]; issue JMP(09)#9; Doikou et al IJMPA(10)-a0912 [introduction, and quantum groups and the quantum inverse scattering method]; Lamers PoS-a1501 [and high-energy physics]; Combot a1609 [general definition of integrability and classification].
@ Quantization of classical integrable systems: Garay & van Straten a0802 [sufficient condition]; Marino & Nekhoroshev a1001, a1001; Sharygin & Talalaev a1210 [deformation quantization].
@ Related topics: Baldo & Raciti qp/95 [eigenstates along trajectories]; Scotti & Ushveridze JMP(97)qp/96 [non-linear quantization]; Kay PRA(04) [wave functions]; > s.a. Inverse Scattering.

Types and Examples
* Examples: Calogero-type (rational) & Sutherland-type (trigonometric).
@ Calogero-Sutherland: Garcia et al JPA(01)mp [raising/lowering]; Langmann CMP(04)mp/01 [second quantization].
@ Bi-Hamiltonian systems: Cariñena et al IJMPA(00)mp/06; Marmo et al JPA(05), TMP(05)mp, NdM(04)mp/05 [and compatible Hermitian structures]; > s.a. symplectic structures.
@ Other examples: Calogero & van Diejen JMP(96); Haschke & Ruehl LNP(00)ht/98 [construction]; Rodriguez & Winternitz JMP(02)mp/01 [in En]; Yonezawa & Tsutsui JMP(06) [N = 3 Calogero, inequivalent]; Danilov & Nagaitsev a1111 [and Ermakov transfrmations].
@ Field theories: Schroer a1109 [dynamical and kinematical integrability]; Bostelmann & Cadamuro a1402 [characterization of local observables]; Lamers PoS-a1506 [pedagogical, and high-energy physics].


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