Energy spectrum, potential and inertia functions of a generalizedf-oscillator

Abstract

We consider a generalized four-parameter q-algebra AA† − qγA†A = qαN+β, [N, A] = −A, [N, A†] = A†, associating with operators A and A† the nonlinear f-oscillator operators, defined in terms of the usual harmonic oscillator operators as A ≡ af(N) and A† ≡ f*(N)a† (where a and a† are operators of the Weyl–Heisenberg algebra and N = a†a). The function f(N) is determined from the commutation relations. We write the Hamiltonian for the free f-oscillator and obtain its energy spectrum. Besides, expressing the Hamiltonian in terms of coordinate and momentum, we determine the potential and inertia functions (coordinate-dependent mass) and analyse their behaviour by varying the parameters.