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Supersymmetry of PT-symmetric tridiagonal hamiltonians

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GRADUATE SCHOOL OF SCIENCES AND ENGINEERING

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We extend the study of supersymmetric tridiagonal Hamiltonians to the case of non-Hermitian Hamiltonians with real or complex conjugate eigenvalues. We find the relation between matrix elements of the non-Hermitian Hamiltonian H and its supersymmetric partner H+ in a given basis. Moreover, the orthogonal polynomials in the eigenstate expansion problem attached to H+ can be recovered from those polynomials arising from the same problem for H with the help of kernel polynomials. Besides its generality, the developed formalism in this work is a natural home for using the numerically powerful Gauss quadrature techniques in probing the nature of some physical quantities such as the energy spectrum of PT-symmetric complex potentials. Finally, we solve the shifted PT-symmetric Morse oscillator exactly in the tridiagonal representation.

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World Scientific Publ Co Pte Ltd

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Astronomy, Astrophysics, Physics, nuclear, Physics, particles and fields, Physics, mathematical

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Modern Physics Letters A

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10.1142/S0217732321502424

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