Kasım, Rıfat Mir
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Mir-Kasimov, R.
Mir-Kasimov, Rufat M.
Kasimov, Rifat Mir
Mir-Kasimov, R. M.
Mir-Kasimov, Rufat M.
Kasimov, Rifat Mir
Mir-Kasimov, R. M.
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04.02. Department of Mathematics
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Former Staff
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Documents
42
Citations
466
h-index
10
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Scholarly Output
8
Articles
2
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21680/2634
Supervised MSc Theses
2
Supervised PhD Theses
0
WoS Citation Count
20
Scopus Citation Count
20
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0
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0
WoS Citations per Publication
2.50
Scopus Citations per Publication
2.50
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7
Supervised Theses
2
| Journal | Count |
|---|---|
| Czechoslovak Journal of Physics | 3 |
| Foundations of Physics | 1 |
| Group 24 : Physical and Mathematical Aspects of Symmetries | 1 |
| Progress of Theoretical Physics | 1 |
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8 results
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Now showing 1 - 8 of 8
Master Thesis Fourier Analysis on the Lorentz Group and Relativistic Quantum Mechanics(Izmir Institute of Technology, 2008) Ok, Zahide; Kasım, Rıfat Mir; Kasım, Rıfat MirThe non-relativistic Schrödinger and Lippman-Schwinger equations are described. The expressions of these equations are investigated in momentum and configuration spaces, using Fourier transformation. The plane wave, which is generating function for the matrix elements of three dimensional Euclidean group in spherical basis, expanded in terms of Legendre polynomials and spherical Bessel functions. Also explicit calculation of Green.s function is done.The matrix elements of the unitary irreducible representations of Lorentz group are used to introduce Fourier expansion of plane waves. And the kernel of Gelfand-Graev transformation, which is the relativistic plane wave, is expanded in to these matrix elements. Then relativistic differential difference equation in configuration space is constructed.Lippman-Schwinger equations are studied in Lobachevsky space (hyperbolic space). An analogous to the non-relativistic case, using the finite difference Schrödinger equation, one dimensional Green.s function is analyzed for the relativistic case . Also the finite difference analogue of the Heavyside step function is investigated.Conference Object On the Relativistic Supersymmetric Quantum Mechanics(Springer Verlag, 2002) Mir-Kasimov, Rufat M.; Kasım, Rıfat MirThe present paper is devoted to the one-dimensional relativistic supersymmetric quantum mechanics (RSUSYQM). A short formulation of RSUSYQM is given. We show that RSUSYQM is a q-deformed non-relativistic SUSYQM. Two simple examples are given.Master Thesis Non-integer order derivatives(Izmir Institute of Technology, 2007) Gökçen, Murat; Kasimov, Rifat MirThis thesis is devoted to integrals and derivatives of arbitrary order and applications of the described methods in various fields. This study intends to increase the accessibility of fractional calculus by combining an introduction to the mathematics with a review of selected recent applications in physics. It is described general definitions of fractional derivatives. This definitions are compared with their advantages and disadvantages. Fractional calculus concerns the generalization of differentiation and integration to non-integer (fractional) orders. The subject has a long mathematical history being discussed for the first time already in the correspondence of G. W. Leibnitz around 1690. Over the centuries many mathematicians have built up a large body of mathematical knowledge on fractional integrals and derivatives. Although fractional calculus is a natural generalization of calculus, and although its mathematical history is equally long, it has, until recently, played a negligible role in physics. In the first chapter, Grünwald-Letnikov approache to generalization of the notion of the differentation and integration are considered. In the second chapter, the Riemann Liouville definition is given and it is compared with Grünwald-Letnikov definition. The last chapter, Caputo.s definition is given. In appendices, two applications are given including tomography and solution of Bessel equation.Conference Object Citation - WoS: 1Citation - Scopus: 1The Newton-Wigner Localization Concept and Noncommutative Space(Springer Verlag, 2005) Mir-Kasimov, Rufat M.In the formulation of the Newton-Wigner postulates for the relativistic localized states the hypothesis of commutativity of the position operator components is silently accepted as an evident fact. In the present work it is shown that commutativity is not necessary condition and the alternative (noncommutative) approach to the relativistic position operator and localization concept can be realized in a framework of the physically as well as mathematically comprehensive scheme.Article Citation - WoS: 9Citation - Scopus: 10Relation Between Relativistic and Non-Relativistic Quantum Mechanics as Integral Transformation(Springer Verlag, 2002) Mir-Kasimov, Rufat M.A formulation of quantum mechanics (QM) in the relativistic configurational space (RCS) is considered. A transformation connecting the non-relativistic QM and relativistic QM (RQM) has been found in an explicit form. This transformation is a direct generalization of the Kontorovich-Lebedev transformation. It is shown also that RCS gives an example of non-commutative geometry over the commutative algebra of functions.Conference Object Holomorphic Realization of Non-Commutative Space-Time and Gauge Invariance(IOP Publishing, 2003) Mir-Kasimov, Rufat M.The realization of the Poincare Lie algebra in terms of noncommutative differential calculus over the commutative algebra of functions is considered. The algebra of functions is defined on the spectrum of the unitary irreducible representations of the De Sitter group. Corresponding space-time carries the noncommutative geometry. Gauge invariance principle consistent with this noncommutative space is considered.Conference Object On Classical and Quantum Q-Oscillators in the Relativistic Theory(Springer Verlag, 2004) Mir-Kasimov, Rufat M.The factorization method, applied to the finite-difference Schrödinger equation in the relativistic configurational space, allows to consider the q-deformations as a relativistic effect. In particular, different factorizations allow to obtain all known q-oscillators in a unified way. The classical limit of deformed Hamiltonians is investigated.Article Citation - WoS: 10Citation - Scopus: 9Q-Deformed and C-Deformed Harmonic Oscillators(Yukawa Institute for Theoretical Physics, 2003) Sogami, Ikuo S.; Koizumi, Kouzou; Mir-Kasimov, Rufat M.Hamilton functions of classical deformed oscillators (c-deformed oscillators) are derived from Hamiltonians of g-deformed oscillators of the Macfarlane and Dubna types. A new scale parameter, lq, with the dimension of length, is introduced to relate a dimensionless parameter characterizing the deformation with the natural length of the harmonic oscillator. Contraction from q-deformed oscillators to c-deformed oscillators is accomplished by keeping lq finite while taking the limit ℏ → 0. The c-deformed Hamilton functions for both types of oscillators are found to be invariant under discrete translations: the step of the translation for the Dubna oscillator is half of that for the Macfarlane oscillator. The c-deformed oscillator of the Macfarlane type has propagating solutions in addition to localized ones. Reinvestigation of the g-deformed oscillator carried out in the light of these findings for the c-deformed systems proves that the g-deformed systems are invariant under the same translation symmetries as the c-deformed systems and have propagating waves of the Bloch type