Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-08-15
Phys.Lett. B517 (2001) 210-214
Physics
High Energy Physics
High Energy Physics - Theory
10 pages, no figure, accepted by Phys. Lett. B
Scientific paper
10.1016/S0370-2693(01)00964-9
Corresponding to two ways of realizing the q-deformed Heisenberg algebra by the undeformed variables there are two q-perturbative Hamiltonians with the additional momentum-dependent interactions, one originates from the perturbative expansion of the potential, the other originates from that of the kinetic energy term. At the level of operators, these two q-perturbative Hamiltonians are different. In order to establish a reliable foundation of the perturbative calculations in q-deformed dynamics, except examples of the harmonic-oscillator and the Morse potential demonstrated before, the general q-perturbative equivalent theorem is demonstrated, which states that for any regular potential which is singularity free the expectation values of two q-perturbative Hamiltonians in the eigenstates of the undeformed Hamiltonian are equivalent. For the q-deformed ``free'' particle case, the perturbative Hamiltonian originated from the kinetic energy term still keeps its general expression, but it does not lead to energy shift.
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