Exactly solvable quantum-mechanical systems on lattices associated with classical Lie algebras

1985 ◽  
Vol 28 (4) ◽  
pp. 539-549 ◽  
Author(s):  
N. Yu. Reshetikhin
Keyword(s):  
Lie Algebras ◽  
Mechanical Systems ◽  
Quantum Mechanical ◽  
Exactly Solvable ◽  
Solvable Quantum ◽  
Quantum Mechanical Systems

scholarly journals Numerical study of the SWKB condition of novel classes of exactly solvable systems

2020 ◽  
pp. 2150025
Author(s):  
Yuta Nasuda ◽  
Nobuyuki Sawado
Keyword(s):  
Orthogonal Polynomial ◽  
Jacobi Polynomials ◽  
Numerical Study ◽  
Mechanical Systems ◽  
The Other ◽  
Quantum Mechanical ◽  
Shape Invariance ◽  
Exactly Solvable ◽  
Solvable Quantum ◽  
Quantum Mechanical Systems

The supersymmetric WKB (SWKB) condition is supposed to be exact for all known exactly solvable quantum mechanical systems with the shape invariance. Recently, it was claimed that the SWKB condition was not exact for the extended radial oscillator, whose eigenfunctions consisted of the exceptional orthogonal polynomial, even the system possesses the shape invariance. In this paper, we examine the SWKB condition for the two novel classes of exactly solvable systems: one has the multi-indexed Laguerre and Jacobi polynomials as the main parts of the eigenfunctions, and the other has the Krein–Adler Hermite, Laguerre and Jacobi polynomials. For all of them, one can always remove the [Formula: see text]-dependency from the condition, and it is satisfied with a certain degree of accuracy.

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