Quantum isotonic nonlinear oscillator as a Hermitian counterpart of Swanson Hamiltonian and pseudo-supersymmetry

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Yesiltas Ö.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol.44, no.30, 2011 (SCI-Expanded) identifier identifier


Within the ideas of pseudo-supersymmetry, we have studied a non-Hermitian Hamiltonian H(-) = omega(xi(dagger)xi + 1/2) + alpha xi(2) + beta xi(dagger 2), where alpha not equal beta and xi is a first-order differential operator, to obtain the partner potentials V(+)(x) and V(-)(x) which are new isotonic and isotonic nonlinear oscillators, respectively, as the Hermitian equivalents of the non-Hermitian partner Hamiltonians H(+/-). We have provided an algebraic way to obtain the spectrum and wavefunctions of a nonlinear isotonic oscillator. The solutions of V(-)(x) which are Hermitian counterparts of Swanson Hamiltonian are obtained under some parameter restrictions that are found. Also, we have checked whether the intertwining operator satisfies eta(1)H(-) = H(+)eta(1), where eta(1) = rho(-1) A rho and A is the first-order differential operator, which factorizes Hermitian equivalents of H(+/-).