Rationally Extended Harmonic Oscillator potential, Isospectral Family and the Uncertainity Relations

• URL: http://arxiv.org/abs/2304.11314v1
• Date: Sat, 22 Apr 2023 04:44:28 GMT
• Title: Rationally Extended Harmonic Oscillator potential, Isospectral Family and the Uncertainity Relations
• Authors: Rajesh Kumar, Rajesh Kumar Yadav and Avinash Khare
• Abstract summary: We consider the rationally extended harmonic potential which is isospectral to the conventional one. The uncertainty relations for the entire isospectral family potentials for different $m$ and $lambda$ are also calculated.
• Score: 2.640012432639427
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider the rationally extended harmonic oscillator potential which is isospectral to the conventional one and whose solutions are associated with the exceptional, $X_m$- 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 $(\lambda)$ family of exactly solvable isospectral potential corresponding to this extended harmonic oscillator potential is obtained. Special cases corresponding to the $\lambda=0$ and $\lambda = -1$, 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 $\lambda$ are also calculated.

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