Generalized intelligent states and squeezing. (English) Zbl 0824.47056
Summary: The Robertson-Schrödinger uncertainty relation for two observables \(A\) and \(B\) is shown to be minimized in the eigenstates of the operator \(\lambda A+ iB\), \(\lambda\) being a complex number. Such states, called generalized intelligent states (GIS), can exhibit arbitrarily strong squeezing of \(A\) or \(B\). The time evolution of GIS is stable for Hamiltonians which admit invariants linear in \(A\) and \(B\). Systems of GIS for the SU(1,1) and SU(2) groups are constructed and discussed. It is shown that SU(1,1) GIS contain all the Perelomov coherent states (CS) and the Barut and Girardello CS while the spin CS are a subset of SU(2) GIS. CS for an arbitrary semisimple Lie group can be considered as a GIS for the quadratures of the Weyl generators.
MSC:
| 47N50 | Applications of operator theory in the physical sciences |
| 81V10 | Electromagnetic interaction; quantum electrodynamics |
| 81R30 | Coherent states |
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
Keywords:
Robertson-Schrödinger uncertainty relation; eigenstates; generalized intelligent states; strong squeezing; Hamiltonians; semisimple Lie group; quadratures of the Weyl generatorsReferences:
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