Abstract
The metric operator, which is the basic ingredient for studying a quantum system described by a pseudo-Hermitian Hamiltonian, provides the necessary means for obtaining an equivalent description of the system using a Hermitian Hamiltonian. In the framework of supersymmetric quantum mechanics, we propose a method of constructing the metric operator and to obtain the Hermitian Hamiltonian equivalent to the given pseudo-Hermitian.
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References
C. M. Bender, D. C. Brody, and H. F. Jones, Phys. Rev. Lett. 89, 270401 (2002).
C. M. Bender, D. C. Brody, and H. F. Jones, Am. J. Phys. 71, 1095 (2003).
V. Jakubský, Acta Polytech. 47, 71 (2007).
A. Mostafazadeh, J. Math. Phys. 43, 205 (2002).
A. Mostafazadeh, J. Math. Phys. 43, 2814 (2002).
A. Mostafazadeh, J. Math. Phys. 43, 3944 (2002).
A. Mostafazadeh, Class. Quantum Grav. 20, 155 (2003).
C.M. Bender, P. N. Meisinger, and Q. Wang, J. Phys. A 36, 1973 (2003).
C. M. Bender, J. Brod, A. Refig, and M. E. Reuter, J. Phys. A 37, 10139 (2004).
C. M. Bender, D. C. Brody, and H. F. Jones, Phys. Rev. Lett. 93, 251601 (2004).
C. M. Bender, D. C. Brody, and H. F. Jones, Phys. Rev. D 70, 025001 (2004).
C. M. Bender, D. C. Brody, and H. F. Jones, Phys. Rev. D 71, 049901 (Erratum) (2005).
A. Mostafazadeh and A. Batal, J. Phys. A 37, 11645 (2004).
A. Mostafazadeh, J. Phys. A 38, 6557 (2005).
C. M. Bender, I. Cavero-Pelaez, K. A. Milton, and K. V. Shajesh, Phys. Lett. B 613, 97 (2005).
T. V. Fityo, J. Phys. A 35, 5893 (2002).
O. Mustafa and S. H. Mazharimousavi, Phys. Lett. A 357, 295 (2006).
U. Gunther and B. F. Samsonov, Phys. Rev. A 78, 042115 (2008).
A. Mostafazadeh, J. Math. Phys. 43, 6343 (2002).
B.F. Samsonov, V. V. Shamshutdinova, and A. V. Osipov, Phys. Lett. A 374, 1962 (2010).
B. F. Samsonov, J. Phys. A 43, 402006 (2010).
B. M. Levitan and I. S. Sargsyan, Introduction to Spectral Theory: Selfadjoint Ordinary Differential Operators, Translations of Mathematical Monographs (Providence, Rhode Island, 1975).
A. A. Andrianov, F. Cannata, J.-P. Dedonder, and M. V. Ioffe, Int. J. Mod. Phys. A 14, 2675 (1999).
F. Cannata, G. Junker, and J. Trost, Phys. Lett. A 246, 219 (1998).
F. Cannata, M. V. Ioffe, R. Roychoudhury, and P. Roy, Phys. Lett. A 281, 305 (2001).
A. A. Andrianov, F. Cannata, and A. V. Sokolov, Nucl. Phys. B 773, 107 (2007).
A. V. Sokolov, Nucl. Phys. B 773, 137 (2007).
B. F. Samsonov, J. Phys. A 38, L397 (2005).
B. F. Samsonov and P. Roy, J. Phys. A 38, L249 (2005).
D. Krejčiřík, H. Bíla, and M. Znojil, J. Phys. A 39, 10143 (2006).
D. Krejčiřík, J. Phys. A 41, 244012 (2008).
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Shamshutdinova, V.V. Construction of the metric and equivalent Hermitian Hamiltonian via SUSY transformation operators. Phys. Atom. Nuclei 75, 1294–1298 (2012). https://doi.org/10.1134/S1063778812100183
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DOI: https://doi.org/10.1134/S1063778812100183