The uncertainty way of generalization of coherent states. (English) Zbl 1072.81538

Trifonov, Dimitar A.

Mladenov, I. M. (ed.) et al., Proceedings of the international conference on geometry, integrability and quantization, Varna, Bulgaria, September 1–10, 1999. Sofia: Coral Press Scientific Publishing (ISBN 954-90618-1-7/pbk). 257-282 (2000).

The paper considers different ways of generalisations of the classic coherent states (CS) in quantum mechanics. The three main definitions of CS are: (i) as eigenvectors of the boson destruction operator; (ii) as an orbit of certain group representation; (iii) as vectors minimising the uncertainty relation. There is an overview of the current state of art of the first two approaches but the main attention is given to the third route. The uncertainty inequalities are used in the Schrödinger and Robertson forms. Considered examples are standard \(SU(1,1)\) and \(SU(2)\) coherent states and a set of states which minimise the Schrödinger inequality for the Hermitian components of the \(su_q(1,1)\) ladder operator.
For the entire collection see [Zbl 0940.00039].

Reviewer: Vladimir V. Kisil (Leeds)

MSC:

81R30

Coherent states

Keywords:

coherent state; squeezed state; uncertainty state; group representations; uncertainty relation; Schrödinger inequality; Robertson inequality; creation operator; annihilation operator; destruction operator