A generalized method which helps to find a time-dependent SchrÖdinger
equation for any static potential is established. We illustrate this method
with two examples. Indeed, we use this method to find the time-dependent
Hamiltonian of quasi-exactly solvable Lamé equation and to construct the matrix
2 × 2 time-dependent polynomial Hamiltonian.
References
[1]
Finkel, F. and Kamran, N. (1997) Quasi-exactly solvable time-dependent potentials. arXiv:physics/9705022 [math-ph]
[2]
Turbiner, A.V. (1988) Quasi-Exactly-Solvable Problems and sl(2) Algebra. Communications in Mathematical Physics, 118, 467-474. http://dx.doi.org/10.1007/BF01466727
[3]
Ushveridze, A. (1989) Quasi-Exactly Solvable Models in Quantum Mechanics. Soviet Journal of Nuclear Physics, 20, 504-528.
[4]
Brihaye, Y. and Kosinski, P. (1999) Weak-Qes Extensions of the Calogero Model. Modern Physics Letters A, 14, 2579-2585. http://dx.doi.org/10.1142/S0217732399002704
[5]
Brihaye, Y., Ndimubandi, J. and Prasad Mandal, B. (2007) QES Systems, Invariant Spaces and Polynomials Recursions. International Journal of Modern Physics A, A22, 1423.
[6]
Brihaye, Y., Nininahazwe, A. and Prasad Mandal, B. (2007) PT-Symmetric, Quasi-Exactly Solvable Matrix Hamiltonians. Journal of Physics A: Mathematical and Theoretical, 40, 130063-130073.
[7]
Brihaye, Y. and Godard, M. (1993) Quasi Exactly Solvable Extensions of the Lamé Equation. Journal of Mathematical Physics, 34, 5283. http://dx.doi.org/10.1063/1.530304
[8]
Brihaye, Y. and Hartmann, B. (2001) Modern Physics Letters A, 16, 1985-1906.
