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On Generalized Fractional Spin, Fractional Angular Momentum, Fractional Momentum Operators in Quantum Mechanics

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Abstract

In this study, we have extended the idea of fractional spin introduced recently in literature based on two orders fractional derivative operator. Generalizations of the fractional spin, the fractional angular momentum and the fractional momentum operators were obtained. The theory is characterized by a noncommutativity between the generalized fractional angular momentum and the fractional Hamiltonian. We have derived the corresponding fractional Schrödinger equation and we have discussed its implications on the problems of a free particle and a particle moving in an infinite well potential. Enhancements of their corresponding energies levels and ground energies were observed which are in agreement with phenomenological theories such as noncommutative quantum mechanics.

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References

  1. R. Herrmann, Fractional Calculus: An Introduction for Physicists (World Scientific Publishing Company, Singapore, 2011)

    MATH  Google Scholar 

  2. K. Miller, B. Ross, An Introduction to Fractional Calculus and Fractional Differential Equations (Wiley, New York, 1993)

    MATH  Google Scholar 

  3. K.B. Oldham, J. Spanier, The Fractional Calculus (Dover Publications, Mineola, 2006)

    MATH  Google Scholar 

  4. I. Podlubny, Fractional Differential Equations (Academic Press, New York, 1999)

    MATH  Google Scholar 

  5. R.A. El-Nabulsi, Fractional functional with two occurrences of integrals and asymptotic optimal change of drift in the Black-Scholes model. Acta Math. Viet. 40, 689–703 (2015)

    MathSciNet  MATH  Google Scholar 

  6. L. Sommacal, P. Melchior, A. Oustaloup, J.-M. Cabelguen, A.J. Ijspeert, Fractional multi-models of the frog gastrocnemius muscle. J. Vib. Control 14, 1415–1430 (2008)

    MATH  Google Scholar 

  7. R.A. El-Nabulsi, Fractional derivatives generalization of Einstein’s field equations. Ind. J. Phys. 87, 195–200 (2013)

    Google Scholar 

  8. N. Heymans, Dynamic measurements in long-memory materials: fractional calculus evaluation of approach to steady state. J. Vib. Control 14, 1587–1596 (2008)

    MATH  Google Scholar 

  9. R.A. El-Nabulsi, Gravitons in fractional action cosmology. Int. J. Theor. Phys. 51, 3978–3992 (2012)

    MathSciNet  MATH  Google Scholar 

  10. R.A. El-Nabulsi, Fractional dynamics, fractional weak bosons masses and physics beyond the standard model. Chaos Solitons Fractals 4, 2262–2270 (2009)

    Google Scholar 

  11. R.A. El-Nabulsi, Modifications at large distances from fractional and fractal arguments. FRACTALS 18, 185–190 (2010)

    MathSciNet  MATH  Google Scholar 

  12. W.M. Ahmad, R. El-Khazali, Fractional-order dynamical models of love. Chaos Solitons Fractals 33, 1367–1375 (2007)

    ADS  MathSciNet  MATH  Google Scholar 

  13. R.A. El-Nabulsi, The fractional white dwarf hydrodynamical nonlinear differential equation and emergence of quark stars. Appl. Math. Comput. 218, 2837–2849 (2011)

    MathSciNet  MATH  Google Scholar 

  14. R.A. El-Nabulsi, Fractional oscillators from non-standard Lagrangians and time-dependent fractional exponent. Comput. Appl. Math. 33, 163–179 (2014)

    MathSciNet  MATH  Google Scholar 

  15. F.B.M. Duarte, J.A.T. Machado, Chaotic phenomena and fractional-order dynamics in the trajectory control of redundant manipulators. Nonlinear Dyn. 29, 315–342 (2002)

    MathSciNet  MATH  Google Scholar 

  16. A.H. Cloot, J.P. Botha, A generalized groundwater flow equation using the concept of non-integer order. Water SA 32, 1–7 (2006)

    Google Scholar 

  17. R.L. Magin, Fractional Calculus in Bioengineering (Begell House, Connecticut, 2006)

    Google Scholar 

  18. R.A. El-Nabulsi, T.A. Soulati, H. Rezazadeh, Non-standard complex Lagrangian dynamics. J. Adv. Res. Dyn. Control Syst. 5, 50–62 (2013)

    MathSciNet  Google Scholar 

  19. R.A. El-Nabulsi, The fractional Boltzman transport equation. Comput. Math. Appl. 62, 1568–1575 (2011)

    MathSciNet  MATH  Google Scholar 

  20. S. Bhalekar, V. Daftardar-Gejji, D. Baleanu, R. Magin, Fractional Bloch equation with delay. Comput. Math. Appl. 61, 1355–1365 (2011)

    MathSciNet  MATH  Google Scholar 

  21. R.A. El-Nabulsi, Fractional variational symmetries of Lagrangians, the fractional Galilean transformation and the modified Schrödinger equation. Nonlinear Dyn. 81, 939–948 (2015)

    MATH  Google Scholar 

  22. D. Ingman, J. Suzdalnitsky, Application of differential operator with servo-order function in model of viscoelastic deformation process. J. Eng. Mech. 131, 763–767 (2005)

    Google Scholar 

  23. R.A. El-Nabulsi, Fractional quantum Euler-Cauchy equation in the Schrödinger picture, complexified harmonic oscillators and emergence of complexified Lagrangian and Hamiltonian dynamics. Mod. Phys. Lett. B 23, 3369–3386 (2009)

    ADS  MATH  Google Scholar 

  24. F. Mainardi, R. Gorenflo, On Mittag-Leffler-type functions in fractional evolution processes. J. Comput. Appl. Math. 118, 283–299 (2000)

    ADS  MathSciNet  MATH  Google Scholar 

  25. R.A. El-Nabulsi, Geostrophic flow and wind-driven ocean currents depending on the spatial dimensionality of the medium. Pure Appl. Geophys. 176, 2739–2750 (2019)

    Google Scholar 

  26. R.A. El-Nabulsi, Fractional Navier-Stokes equation from fractional velocity arguments and its implications in fluid flows and microfilaments. Int. J. Nonlinear Numer. Simul. 20, 449–459 (2019)

    MathSciNet  MATH  Google Scholar 

  27. F. Gómez, J. Bernal, J. Rosales, T. Cordova, Modeling and simulation of equivalent circuits in description of biological systems-a fractional calculus approach. J. Elect. Bioimped. 3, 2 (2012)

    Google Scholar 

  28. R.A. El-Nabulsi, Nonstandard fractional Lagrangians. Nonlinear Dyn. 74, 381–394 (2013)

    MATH  Google Scholar 

  29. R.A. El-Nabulsi, Path integral formulation of fractionally perturbed Lagrangian oscillators on fractal. J. Stat. Phys. 172, 1617–1640 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

  30. R.A. El-Nabulsi, Finite two-point space without quantization on noncommutative space from a generalized fractional integral operator. Compl. Anal. Oper. Theor. 12, 1609–1616 (2018)

    MathSciNet  Google Scholar 

  31. R.C. Koeller, Applications of fractional calculus to the theory of viscoelasticity. J. Appl. Mech. 51, 299–307 (1984)

    ADS  MathSciNet  MATH  Google Scholar 

  32. R.A. El-Nabulsi, Fractional nonlocal Newton’s law of motion and emergence of Bagley–Torvik equation. J Peridyn. Nonlocal Model 2, 50–58 (2020)

    Google Scholar 

  33. J. Ding, H. Zhou, D. Liu, Q. Chen, J. Liu, Research on fractional derivative three elements model of salt rock. Chin. J. Rock Mech. Eng. 33, 672–678 (2014)

    Google Scholar 

  34. R.A. El-Nabulsi, Complexified quantum field theory and “mass without mass” from multidimensional fractional actionlike variational approach with dynamical fractional exponents. Chaos Solitons Fractals 42, 2384–2398 (2009)

    ADS  Google Scholar 

  35. R.A. El-Nabulsi, Fractional Dirac operators and deformed field theory on Clifford algebra. Chaos Solitons Fractals 42, 2614–2622 (2009)

    ADS  MATH  Google Scholar 

  36. Y.J. Song, S.Y. Lei, Mechanical model of rock nonlinear creep damage based on fractional calculus. Chin. J. Underground Space Eng. 9, 91–122 (2013)

    MathSciNet  Google Scholar 

  37. R.A. El-Nabulsi, Emergence of quasiperiodic quantum wave functions in Hausdorff dimensional crystals and improved intrinsic Carrier concentrations. J. Phys. Chem. Sol. 127, 224–230 (2019)

    ADS  Google Scholar 

  38. R.A. El-Nabulsi, Dirac equation with position-dependent mass and Coulomb-like field in Hausdorff dimension. Few-Body Syst. 61, 1–10 (2020)

    ADS  Google Scholar 

  39. R.A. El-Nabulsi, The fractional kinetic Einstein-Vlasov system and its implications in Bianchi spacetimes geometry. Int. J. Theor. Phys. 53, 2712–2726 (2014)

    MathSciNet  MATH  Google Scholar 

  40. R.A. El-Nabulsi, On a new fractional uncertainty relation and its implications in quantum mechanics and molecular physics. Proc. R. Soc. A 476, 20190729 (2020)

    MathSciNet  MATH  Google Scholar 

  41. V.E. Tarasov, Fractional Heisenberg equation. Phys. Lett. A 372, 2984–2988 (2008)

    ADS  MathSciNet  MATH  Google Scholar 

  42. V.E. Tarasov, Fractional generalization of the quantum Markovian master equation. Theor. Math. Phys. 158, 179–195 (2009)

    MathSciNet  MATH  Google Scholar 

  43. R.A. El-Nabulsi, On the fractional minimal uncertainty relation from fractional Riccati generalized momentum operator. Chaos Solitons Fractals 42, 84–88 (2009)

    ADS  MATH  Google Scholar 

  44. V.E. Tarasov, Weyl quantization of fractional derivatives. J. Math. Phys. 49, ID102112 (2008)

    ADS  MathSciNet  Google Scholar 

  45. M. Zubair, M.J. Mughal, Q.A. Naqvi, An exact solution of spherical wave in D-dimensional fractional space. J. Electromagnet. Res. Appl. 25, 1481–1491 (2011)

    Google Scholar 

  46. M. Zubair, M.J. Mughal, Q.A. Naqvi, The wave equation and general plane wave solutions in fractional space. Prog. Electromagnet. Res. Lett. 19, 137–146 (2010)

    Google Scholar 

  47. Q.A. Naqvi, M. Zubair, On cylindrical model of electrostatic potential in fractional dimensional space. Optik Int. J. Light Electron Opt. 127, 3243–3247 (2016)

    Google Scholar 

  48. R.A. El-Nabulsi, Fractional quantum field theory on multifractal sets. Am. J. Eng. Appl. Sci. 4(1), 133–141 (2010)

    MathSciNet  Google Scholar 

  49. R.A. El-Nabulsi, Fractional field theories from multidimensional fractional variational problems. Int. J. Mod. Geom. Meth. Mod. Phys. 5(6), 863–892 (2008)

    MATH  Google Scholar 

  50. R.A. El-Nabulsi, G.-C. Wu, Fractional complexified field theory from Saxena–Kumbhat fractional integral, fractional derivative of order \((\alpha, \beta )\) and dynamical fractional integral exponent. Afr. Disp. J. Math. 13, 45–61 (2012)

    MathSciNet  MATH  Google Scholar 

  51. H. Kleinert, Fractional quantum field theory, path integral, and stochastic differential equation for strongly interacting many-particle systems. Europhys. Lett. 100, 10001 (2012)

    ADS  Google Scholar 

  52. N. Laskin, Fractional quantum mechanics and Levy path integrals. Phys. Lett. A 268, 298–305 (2000)

    ADS  MathSciNet  MATH  Google Scholar 

  53. N. Laskin, Fractional quantum mechanics. Phys. Rev. E 62, 3135–3145 (2000)

    ADS  MATH  Google Scholar 

  54. R.A. El-Nabulsi, Time-fractional Schrodinger equation from path integral and its implications in quantum dots and semiconductors. Europ. Phys. J. P 133, 394 (2018)

    Google Scholar 

  55. G. Calcagni, Geometry of fractional spaces. Adv. Theor. Math. Phys. 16, 549–644 (2012)

    MathSciNet  MATH  Google Scholar 

  56. G. Calcagni, Fractal universe and quantum gravity. Phys. Rev. Lett. 104, 251301 (2010)

    ADS  Google Scholar 

  57. G. Calcagni, G. Nardelli, M. Scalisi, Quantum mechanics in fractional and other anomalous spacetimes. J. Math. Phys. 53, 102110–102125 (2012)

    ADS  MathSciNet  MATH  Google Scholar 

  58. S.C. Lim, Fractional derivative quantum fields at positive temperature. Phys. A 363, 269–281 (2006)

    MathSciNet  Google Scholar 

  59. S.C. Lim, L.P. Teo, Casimir effect associated with fractional Klein–Gordon field, in Fractional Dynamics, ed. by J. Klafter, S.C. Lim, R. Metzler (World Science Publisher, Singapore, 2012), pp. 483–506

    MATH  Google Scholar 

  60. A.K. Golmankhaneh, D. Baleanu, Fractal calculus involving Gauge function. Commun. Nonlinear Sci. 37, 125–130 (2016)

    MathSciNet  Google Scholar 

  61. A.K. Golmankhaneh, D. Baleanu, Non-local integrals and derivatives on fractal sets with applications. Open Phys. 14, 542–548 (2016)

    Google Scholar 

  62. A.K. Golmankhaneh, C. Tunc, On the Lipschitz condition in the fractal calculus. Chaos Solitons Fractals 95, 140–147 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

  63. R.A. El-Nabulsi, Glaeske–Kilbas–Saigo fractional integration and fractional Dixmier trace. Acta Math. Viet. 37, 149–160 (2012)

    MathSciNet  MATH  Google Scholar 

  64. E. Goldfain, Complexity in quantum field theory and physics beyond the Standard Model. Chaos Solitons Fractals 28, 913–922 (2009)

    ADS  MATH  Google Scholar 

  65. E. Goldfain, Fractional dynamics and the standard model for particle physics. Commun. Nonlinear Sci. Numer. Simul. 13, 1397–1404 (2008)

    ADS  MathSciNet  MATH  Google Scholar 

  66. E. Goldfain, Fractional dynamics, Cantorian spacetime and the gauge hierarchy problem. Chaos Solitons Fractal 22, 513–520 (2004)

    ADS  MATH  Google Scholar 

  67. E. Goldfain, Fractional dynamics and the TeV regime of field theory particle. Commun. Nonlinear Sci. Numer. Simul. 13, 666–676 (2008)

    ADS  MathSciNet  MATH  Google Scholar 

  68. R. Herrmann, Folded potentials in cluster physics-a comparison of Yukawa and Coulomb potentials with Riesz fractional integrals. J. Phys. A Math. Theor. 46, 405203 (2013)

    MathSciNet  MATH  Google Scholar 

  69. R.A. El-Nabulsi, Dirac operator of order 2/3 from Glaeske-Kilbas-Saigo fractional integral. Funct. Anal. Approx. Comput. 7, 15–28 (2015)

    MathSciNet  Google Scholar 

  70. V.E. Tarasov, Fractional quantum field theory: from lattice to continuum. Adv. High Energy Phys. 2014, ID957863 (2014)

    MathSciNet  Google Scholar 

  71. R. Herrmann, Fractional spin-a property of particles described with a fractional Schrödinger equation, arXiv: 0805.3434

  72. R. Herrmann, Gauge invariance in fractional field theories. Phys. Lett. A 372, 5515–5522 (2008)

    ADS  MathSciNet  MATH  Google Scholar 

  73. R. Herrmann, The fractional symmetric rigid rotor. J. Phys. G 34, 607–626 (2007)

    ADS  Google Scholar 

  74. R. Herrmann, Fractional dynamic symmetries and the ground state properties of nuclei. Phys. A 389, 693–704 (2010)

    MathSciNet  Google Scholar 

  75. N. Moiseyev, Non-Hermitian Quantum Mechanics (Cambridge University Press, Cambridge, 2011)

    MATH  Google Scholar 

  76. C.M. Bender, S. Boettcher, Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett. 80, 5243 (1998)

    ADS  MathSciNet  MATH  Google Scholar 

  77. D.C. Brody, E.-M. Graefe, On complexified mechanics and coquaternions. J. Phys. A44, 072001 (2011)

    ADS  MathSciNet  MATH  Google Scholar 

  78. R.S. Kaushal, Classical and quantum mechanics of complex Hamiltonian systems: an extended complex phase space approach. PRAMANA J. Phys. 73, 287–297 (2009)

    ADS  Google Scholar 

  79. R.A. El-Nabulsi, On nonlocal complexified Schrödinger equation and emergence of discrete quantum mechanics. Quant. Stud. Math. Found. 3, 327–335 (2016)

    MATH  Google Scholar 

  80. R.A. El-Nabulsi, Quantization of non-standard Hamiltonians and the Riemann zeros. Qual. Theor. Dyn. Syst. 18, 69–84 (2019)

    MathSciNet  MATH  Google Scholar 

  81. S. De Leo, W.A. Rodrigues, Quantum mechanics: from complex to complexified quaternions. Int. J. Theor. Phys. 36, 2725–2757 (1997)

    MathSciNet  MATH  Google Scholar 

  82. G. Guralnik, Z. Guralnik, Complexified path integrals and the phases of quantum field theory. Ann. Phys. 325, 2486–2498 (2010)

    ADS  MathSciNet  MATH  Google Scholar 

  83. S. De Leo, W.A. Rodrigues, Quaternionic electron theory: Dirac’s equation. Int. J. Theor. Phys. 37, 1511–1529 (1998)

    MathSciNet  MATH  Google Scholar 

  84. P.B. Gilkey, J.V. Leahy, J. Park, Spectral Geometry, Riemannian Submersions, and the Gromov-Lawson conjecture, Studies in Advanced Mathematics (Chapman & Hall/CRC, Boca Raton, 1999)

    MATH  Google Scholar 

  85. W.D. Curtis, D.E. Lerner, Complex line bundles in relativity. J. Math. Phys. 19, 874–877 (1978)

    ADS  MathSciNet  MATH  Google Scholar 

  86. R. Penrose, W. Rindler, Spinors and Space-Time, vol. 1 (Cambridge University Press, Cambridge, 1986)

    MATH  Google Scholar 

  87. R. Penrose, W. Rindler, Spinors and Space-Time, vol. 2 (Cambridge University Press, Cambridge, 1988)

    MATH  Google Scholar 

  88. R.S. Ward, R.O. Wells, Twistor Geometry and Field Theory (Cambridge University Press, Cambridge, 1990)

    MATH  Google Scholar 

  89. I.R. Senitzky, Dissipation in quantum mechanics. The harmonic oscillator. Phys. Rev. 119, 670 (1960)

    ADS  MathSciNet  MATH  Google Scholar 

  90. N. Moiseyev, Quantum theory of resonances: calculating energies, widths and cross-sections by complex scaling. Phys. Rep. 302, 212–293 (1998)

    ADS  Google Scholar 

  91. J. Okolowicz, M. Ploszajczak, I. Rotter, Dynamics of quantum systems embedded in a continuum. Phys. Rep. 374, 271–383 (2003)

    ADS  MathSciNet  MATH  Google Scholar 

  92. C.M. Bender, S. Boettcher, Real spectra in non-Hermitian Hamiltonians having P T symmetry. Phys. Rev. Lett. 80, 5243 (1998)

    ADS  MathSciNet  MATH  Google Scholar 

  93. C.M. Bender, Making sense of non-Hermitian Hamiltonians. Rep. Prog. Phys. 70, 947–1018 (2007)

    ADS  MathSciNet  Google Scholar 

  94. A. Mostafazadeh, Pseudo-Hermitian representation of quantum mechanics. Int. J. Geom. Methods Mod. Phys. 07, 1191 (2010)

    MathSciNet  MATH  Google Scholar 

  95. Eva-Maria Graefe, M. Hoening, H.J. Korsch, Classical limit of non-Hermitian quantum dynamics-a generalized canonical structure. J. Phys. A Math. Theor. 43, 7 (2010)

    MathSciNet  Google Scholar 

  96. R.A. El-Nabulsi, Lagrangian and Hamiltonian dynamics with imaginary time. J. Appl. Anal. 18, 283–295 (2012)

    MathSciNet  MATH  Google Scholar 

  97. K. Nigam, K. Banerjee, Quantum dynamics of complex Hamiltonians, arXiv: 1602.00157

  98. C.M. Bender, Complex extension of quantum mechanics. Proc. Inst. Math. NAS Ukraine 50, 617–628 (2004)

    MathSciNet  MATH  Google Scholar 

  99. R.S. Kaushal, Parthasarathi, Quantum mechanics of complex Hamiltonian systems in one dimension. J. Phys. A Math. Gen. 35, 8743 (2002)

    MATH  Google Scholar 

  100. H.M. Nussenzweig, Diffraction Effects in Semi-Classical Physics (Cambridge University Press, Cambridge, 1992)

    Google Scholar 

  101. V. De Alfaro, T. Regge, Potential Scattering (North Holland, Amsterdam, 1965)

    MATH  Google Scholar 

  102. R.G. Newton, The Complex j-Plane (Benjamin, Barbara, 1964)

    MATH  Google Scholar 

  103. J. Bros, G.A. Viano, Complex angular momentum in general quantum field theory. Ann. Henri Poincare 1, 101–172 (2006)

    ADS  MathSciNet  MATH  Google Scholar 

  104. W. Drechsler, Complex angular momentum theory in particle physics. Forts. Phys. 18, 305–448 (1970)

    ADS  Google Scholar 

  105. D. Basu, S.D. Majumdar, Complex angular momenta and the Lorentz group. J. Phys. A Math. Nucl. Gen. 6, 1097 (1973)

    ADS  MATH  Google Scholar 

  106. W.J. Holman, L.C. Biedenharn Jr., Complex angular momenta and the groups SU(1,1) and SU(2). Ann. Phys. 39, 1–42 (1966)

    ADS  MathSciNet  MATH  Google Scholar 

  107. D. Sokolovski, E. Akhmatskaya, C. Echeverrıa-Arrondoa, D. De Fazio, Complex angular momentum theory of state-to-state integral cross sections: resonance effects in the F \(+\) HD ->HF(v \(=\) 3) \(+\) D reaction. Phys. Chem. Chem. Phys. 17, 18577 (2015)

    Google Scholar 

  108. J. Cresson, Fractional embedding of differential operators and Lagrangian systems. J. Math. Phys. 48, 033504 (2007)

    ADS  MathSciNet  MATH  Google Scholar 

  109. S.S. Bayin, Time fractional Schrödinger equation: Fox’s H-functions and the effective potential. J. Math. Phys. 54, 012103 (2013)

    ADS  MathSciNet  MATH  Google Scholar 

  110. E. Capelas de Oliveira, F.S. Costa, J. Vaz Jr., The fractional Schrödinger equation for delta potentials. J. Math. Phys. 51, 123517 (2010)

    ADS  MathSciNet  MATH  Google Scholar 

  111. E. Capelas de Oliveira, J. Vaz Jr., Tunneling in fractional quantum mechanics. J. Phys. A Math. Theor. 44, 185303 (2011)

    ADS  MathSciNet  MATH  Google Scholar 

  112. M. Jeng, S.-L.-Y. Xu, E. Hawkins, J.M. Schwarz, On the nonlocality of the fractional Schrödinger equation. J. Math. Phys. 51, 062102 (2010)

    ADS  MathSciNet  MATH  Google Scholar 

  113. P. Xiang, Y.-X. Guo, J.-L. Fu, Time and space fractional Schrödinger equation with fractional factor. Commun. Theor. Phys. 71, 016 (2019)

    ADS  MathSciNet  Google Scholar 

  114. J. Gamboa, M. Loawe, J.C. Rojas, Non-commutative quantum mechanics. Phys. Rev. D 64, 067901 (2001)

    ADS  MathSciNet  Google Scholar 

  115. C.M. Rohwer, K.G. Zloshchastiev, L. Gouba, F.G. Scholtz, Noncommutative quantum mechanics-a perspective on structure and spatial extent. J. Phys. A Math. Theor. 43, 345303 (2010)

    MathSciNet  MATH  Google Scholar 

  116. R. Herrmann, Properties of a fractional derivative Schrödinger type wave equation and a new interpretation of the charmonium spectrum. arXiv: math-ph/0510099

  117. M. Bawaj, C. Biancofiore, M. Bonaldi, F. Bonfigli, A. Borrielli, G. Di Giuseppe, L. Marconi, F. Marino, R. Natali, R.A. Pontin, G.A. Prodi, E. Serra, D. Vitali, F. Marin, Probing deformed commutators with macroscopic harmonic oscillators. Nat. Commun. 6, 7503–7510 (2015)

    ADS  Google Scholar 

  118. J.-Z. Zhang, Fractional angular momentum in non-commutative spaces. Phys. Lett. B 584, 204–209 (2004)

    ADS  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The author would like to thank the group of anonymous referees for their useful remarks and valuable suggestions.

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  1. Athens Institute for Education and Research, Mathematics and Physics Divisions, 8 Valaoritou Street, Kolonaki, 10671, Athens, Greece

    Rami Ahmad El-Nabulsi

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El-Nabulsi, R.A. On Generalized Fractional Spin, Fractional Angular Momentum, Fractional Momentum Operators in Quantum Mechanics. Few-Body Syst 61, 25 (2020). https://doi.org/10.1007/s00601-020-01558-0

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