Matrix elements of in the Morse oscillator basis

1998 ◽  
Vol 31 (15) ◽  
pp. 3461-3467 ◽  
Author(s):  
Malgorzata Bancewicz
Keyword(s):  
Matrix Elements ◽  
Morse Oscillator ◽  
Oscillator Basis

scholarly journals Supersymmetry of 𝒫𝒯-symmetric tridiagonal Hamiltonians

2021 ◽  
Author(s):  
Mohammad Walid AlMasri
Keyword(s):  
Energy Spectrum ◽  
Orthogonal Polynomials ◽  
Complex Potentials ◽  
Complex Conjugate ◽  
Matrix Elements ◽  
Morse Oscillator ◽  
Supersymmetric Partner ◽  
Natural Home ◽  
Symmetric Complex ◽  
Physical Quantities

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 [Formula: see text] and its supersymmetric partner [Formula: see text] in a given basis. Moreover, the orthogonal polynomials in the eigenstate expansion problem attached to [Formula: see text] can be recovered from those polynomials arising from the same problem for [Formula: see text] 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 [Formula: see text]-symmetric complex potentials. Finally, we solve the shifted [Formula: see text]-symmetric Morse oscillator exactly in the tridiagonal representation.

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