Uncertainty relations for a \(q\)-deformed coherent spin state. (English) Zbl 1255.81180
Summary: A Coherent Spin State (CSS) is defined as an eigenstate of the spin component in the direction specified by angles \((\theta_{0},\varphi_{0})\). This state satisfies minimum uncertainty relation, with uncertainties equally distributed on any two orthogonal components normal to the direction of the total spin vector \(\langle S\rangle \). Starting from this concept, we apply the notion of CSS to quantum groups and discuss the properties of \(q\)-deformed CSS and the associated uncertainty relations. We show that these states behave as Intelligent Spin States (ISS) on two orthogonal components normal to the direction of the mean value of the spin operator.
MSC:
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
| 81R30 | Coherent states |
| 81R25 | Spinor and twistor methods applied to problems in quantum theory |
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