New Version of Q-Deformed Supersymmetric Quantum Mechanics
A new version of the q-deformed supersymmetric quantum mechanics (q-SQM), which is inspired by the Tamm–Dankoff-type (TD-type) deformation of quantum harmonic oscillator, is constructed. The obtained algebra of q-SQM is similar to that in Spiridonov’s approach. However, within our version of q-SQM, the ground state found explicitly in the special case of superpotential yielding q-superoscillator turns out to be non-Gaussian and takes the form of special (TD-type) q-deformed Gaussian.
L.C. Biedenharn, J. Phys. A: Math. Gen. 22, L873, (1989).
A.J. Macfarlane, J. Phys. A: Math. Gen. 22, 4581, (1989).
V. Spiridonov, Mod. Phys. Lett. A 7, 1241, (1992); [hepth/9202013].
E. Witten, Nucl. Phys. B 188, 513 (1981).
L.E. Gendenshtein and I.V. Krive, Sov. Phys. Usp. 28, 645 (1985).
K. Odaka, T. Kishi, and S. Kamefuchi, J. Phys. A: Math. Gen. 24, L591 (1991).
S. Chaturvedi, V. Srinivasan, and R. Jagannathan, Mod. Phys. Lett. A 8, 3727 (1993).
A.M. Gavrilik and A.P. Rebesh, Mod. Phys. Lett. A 22, 949 (2007);
A.M. Gavrilik and A.P. Rebesh, Mod. Phys. Lett. A 22, 949 (2007); A.M. Gavrilik and A.P. Rebesh, Eur. Phys. J. A bf 47, 55 (2011), arXiv: 1007.5187 [quant-ph].
A.A. Andrianov and M.V. Ioffe, J. Phys. A: Math. Theor. 45, 503001 (2012).
G. Gasper and M. Rahman, Basic Hypergeometric Series (Cambridge Univ. Press, Cambridge, 2004).
R. Jagannathan and K. Srinivasa Rao, Two-parameter quantum algebras, twin-basic numbers, and associated generalized hypergeometric series, preprint arXiv: math/0602613.
A.M. Gavrilik and I.I. Kachurik, Mod. Phys. Lett. A 27, No. 21, 1250114 (2012).