|
| related topics |
| {equation, function, exp} |
| {operator, operators, space} |
| {phase, path, phys} |
| {time, decoherence, evolution} |
| {cos, sin, state} |
| {level, atom, field} |
| {group, space, representation} |
| {state, states, coherent} |
| {field, particle, equation} |
| {spin, pulse, spins} |
| {cavity, atom, atoms} |
| {time, wave, function} |
|
Exact solutions of time-dependent three-generator systems
Jian-Qi Shen, Hong-Yi Zhu, Pan Chen
abstract: There exist a number of typical and interesting systems or models which
possess three-generator Lie-algebraic structure in atomic physics, quantum
optics, nuclear physics and laser physics. The well-known fact that all simple
3-generator algebras are either isomorphic to the algebra $sl(2,C)$ or to one
of its real forms enables us to treat these time-dependent quantum systems in a
unified way. By making use of the Lewis-Riesenfeld invariant theory and the
invariant-related unitary transformation formulation, the present paper obtains
exact solutions of the time-dependent Schr\"{o}dinger equations governing
various three-generator quantum systems. For some quantum systems whose
time-dependent Hamiltonians have no quasialgebraic structures, we show that the
exact solutions can also be obtained by working in a sub-Hilbert-space
corresponding to a particular eigenvalue of the conserved generator (i.e., the
time-independent invariant that commutes with the time-dependent Hamiltonian).
The topological property of geometric phase factors in time-dependent systems
is briefly discussed.
- oai_identifier:
- oai:arXiv.org:quant-ph/0205170
- categories:
- quant-ph
- comments:
- 16 pages,no figer
- arxiv_id:
- quant-ph/0205170
- created:
- 2002-05-27
Full article ▸
|
|
| related documents |
| 0509034v1 |
| 0012023v1 |
| 0004019v2 |
| 0406158v1 |
| 9805036v1 |
| 9609019v2 |
| 9709039v1 |
| 0011062v3 |
| 0606006v1 |
| 0201016v1 |
| 0309023v1 |
| 0408048v1 |
| 0605104v1 |
| 0012039v1 |
| 0701227v2 |
| 0202161v1 |
| 0304043v1 |
| 0210120v2 |
| 9812005v1 |
| 0009029v3 |
| 0609023v1 |
| 0406167v2 |
| 0406092v1 |
| 0403019v1 |
| 0209119v1 |
|