2023/04/22 by Rajesh Kumar, Rajesh Kumar Yadav, Kumar, Rajesh +3
Decision Sciences · Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Scientific Measurement and Uncertainty Evaluation
paper · pdf · doi:10.48550/arxiv.2304.11314
openalex publication_date 2023/04/22 · openalex created_date 2023/04/27 · openalex updated_date 2026/07/28
We consider the rationally extended harmonic oscillator potential which is isospectral to the conventional one and whose solutions are associated with the exceptional, Xm- Hermite polynomials and discuss its various important properties for different even codimension of m. The uncertainty relations are obtained for different m and it is shown that for the ground state, the uncertainity increases as m increases. A one parameter (λ) family of exactly solvable isospectral potential corresponding to this extended harmonic oscillator potential is obtained. Special cases corresponding to the λ=0 and λ= -1, which give the Pursey and the Abhram-Moses potentials respectively, are discussed. The uncertainty relations for the entire isospectral family of potentials for different m and λ are also calculated.