Use of classical Fourier amplitudes as quantum matrix elements: a comparison of Morse oscillator Fourier coefficients with quantum matrix elements

1987 ◽  
Vol 91 (9) ◽  
pp. 2258-2267 ◽  
Author(s):  
Randall B. Shirts
Keyword(s):  
Fourier Coefficients ◽  
Matrix Elements ◽  
Morse Oscillator ◽  
Quantum Matrix

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.

Hypervirial calculations of Morse oscillator matrix elements

1983 ◽  
Vol 78 (7) ◽  
pp. 4792-4793 ◽  
Author(s):  
A. Requena ◽  
R. Peña ◽  
J. Zúñiga
Keyword(s):  
Matrix Elements ◽  
Morse Oscillator

Matrix elements for anharmonic potentials: Application to I2 morse oscillator

1986 ◽  
Vol 7 (2) ◽  
pp. 208-212 ◽  
Author(s):  
G. Delgado-barrio ◽  
A. M. Cortina ◽  
A. Varadé ◽  
P. Mareca ◽  
P. Villarreal ◽  
...  
Keyword(s):  
Matrix Elements ◽  
Morse Oscillator
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