arXiv subjects

B. Demircioglu

Publications and source records attributed to B. Demircioglu.

4 recordsLinked to original sources

arXiv2007

Wigner functions, coherent states, one-dimensional marginal probabilities and uncertainty structures of Landau levels

Following an approach based on generating function method phase space characteristics of Landau system are studied in the autonomous framework of deformation quantization. Coherent state property of generating functions is established and marginal probability densities along canonical coordinate lines are derived. Well defined analogs of inner product, Cauchy-Bunyakowsy-Schwarz inequality and state functional have been defined in phase space and they have been used in analyzing the uncertainty structures. The general form of the uncertainty relation for two real-valued functions is derived and uncertainty products are computed in states described by Wigner functions. Minimum uncertainty state property of the standard coherent states is presented and uncertainty structures in the case of phase space generalized coherent states are analyzed.

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arXiv2006

$\hbar$-independent Universality of the Quantum-Classical Canonical Transformations

A theory of non-unitary-invertible as well as unitary canonical transformations is formulated in the context of Weyl's phase space representations. That all quantum canonical transformations without an explicit $\hbar$ dependence are also classical mechanical and vice versa is demonstrated in the phase space. Contrary to some earlier results, it is also shown that the quantum generators and their classical counterparts are identical and $\hbar$-independent. The latter is a powerful result bringing the theory of classical canonical transformations and the $\hbar$-independent quantum ones on an equal footing.

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arXiv2003

Autonomous generation of all Wigner functions and marginal probability densities of Landau levels

Generation of Wigner functions of Landau levels and determination of their symmetries and generic properties are achieved in the autonomous framework of deformation quantization. Transformation properties of diagonal Wigner functions under space inversion, time reversal and parity transformations are specified and their invariance under a four-parameter subgroup of symplectic transformations are established. A generating function for all Wigner functions is developed and this has been identified as the phase-space coherent state for Landau levels. Integrated forms of generating function are used in generating explicit expressions of marginal probability densities on all possible two dimensional phase-space planes. Phase-space realization of unitary similarity and gauge transformations as well as some general implications for the Wigner function theory are presented.

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arXiv2002

Two families of superintegrable and isospectral potentials in two dimensions

As an extension of the intertwining operator idea, an algebraic method which provides a link between supersymmetric quantum mechanics and quantum (super)integrability is introduced. By realization of the method in two dimensions, two infinite families of superintegrable and isospectral stationary potentials are generated. The method makes it possible to perform Darboux transformations in such a way that, in addition to the isospectral property, they acquire the superintegrability preserving property. Symmetry generators are second and fourth order in derivatives and all potentials are isospectral with one of the Smorodinsky-Winternitz potentials. Explicit expressions of the potentials, their dynamical symmetry generators and the algebra they obey as well as their degenerate spectra and corresponding normalizable states are presented.

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