Integrable Quantum Systems

In General > s.a. coherent states; integrable classical system; non-commutative theories; potential [exactly solvable, etc].
* Energy eigenvalues: The Es of the tori whose actions in the semiclassical limit are of the form (n+k/8) h, n arbitrary, k some fixed integer [KAM theory; & Einstein; Brillouin; Keller; Maslov].
@ General references: Kundu ht/96, ht/97-in [rev]; Prykarpatsky & Mykytiuk 98 [geometric]; Hikami & Wadati JMP(03); Clemente-Gallardo & Marmo IJGMP(09)-a0808 [towards a definition]; issue JMP(09)#9.
@ Related topics: Baldo & Raciti qp/95 [eigenstates along trajectories]; Scotti & Ushveridze JMP(97)qp/96 [non-linear quantization]; Kay PRA(04) [wave functions]; Garay & van Straten a0802 [sufficient condition]; > 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].

main page – abbreviations – journals – comments – other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 11 oct 2009