Revisiting an isospectral extension of the Morse potential

Revisiting (quasi-)exactly solvable rational extensions of the Morse potential

The construction of rationally-extended Morse potentials is analyzed in the framework of first-order supersymmetric quantum mechanics. The known family of extended potentials $V_{A,B,{\rm ext}}(x)$, obtained from a conventional Morse potential $V_{A-1,B}(x)$ by the addition of a bound state below the spectrum of the latter, is re-obtained. More importantly, the existence of another family of extended potentials, strictly isospectral to $V_{A+1,B}(x)$, is pointed out for a well-chosen range of parameter values. Although not shape invariant, such extended potentials exhibit a kind of `enlarged' …

Generation of a Novel Exactly Solvable Potential

We report a new shape invariant (SI) isospectral extension of the Morse potential. Previous investigations have shown that the list of "conventional" SI superpotentials that do not depend explicitly on Planck's constant $\hbar$ is complete. Additionally, a set of "extended" superpotentials has been identified, each containing a conventional superpotential as a kernel and additional $\hbar$-dependent terms. We use the partial differential equations satisfied by all SI superpotentials to find a SI extension of Morse with novel properties. It has the same eigenenergies as Morse but different asym…

Revisiting " Morse potential on Quantum Computer for Molecules and Supersymmetric Quantum Mechanics" arxiv:2102.05102v1[quant-physics]

We find theoretical results on energy eigenvalues and corresponding supersymmetric Hamiltonians reflect contradictory behavior for negative values of A. furthermore the resulting supersymmetric partners potentials can be model scattering states instead of bound states, However following the literature ( Flu 1979);J and A (J. Physics A 2020), we suggest a correct form of super potential , which remains valid for both positive and negative values of constants. A from this in complex space also the eigenvalues remain invariant without discussion of T-symmetry as the previous discussion appears in…

Revisiting generalized Hulthén potentials

A relation between the deformed Hulthén potential and the Eckart one is used to write the bound-state wavefunctions of the former in terms of Jacobi polynomials and to calculate their normalization coefficients. The shape invariance property of the Eckart potential in standard first-order supersymmetric quantum mechanics allows to easily rederive the set of extended deformed Hulthén potentials, recently obtained by using the Darboux-Crum transformation, and to show that their spectra and normalized wavefunctions follow without any further calculation. Furthermore, by taking advantage of other …

具有狄拉克δ相互作用的等谱势：受约束谱

Isospectral potentials with Dirac delta interaction: Constrained Spectra

该研究通过不连续超势构造含狄拉克δ函数的等谱量子势，利用边界约束截断能谱，证实局域奇异性可调控量子系统离散能谱，为相关物理系统提供了新途径。

Morse potential in relativistic contexts from generalized momentum operator, Pekeris approximation revisited and mapping

In this work we explore a generalization of the Dirac and Klein-Gordon (KG) oscillators, provided with a deformed linear momentum inspired in nonextensive statistics, that gives place to the Morse potential in relativistic contexts by first principles. In the (1+1)-dimensional case the relativistic oscillators are mapped into the quantum Morse potential. Using the Pekeris approximation, in the (3+1)-dimensional case we study the thermodynamics of the S-waves states (l=0) of the H2, LiH, HCl and CO molecules (in the non-relativistic limit) and of a relativistic electron, where Schottky anomalie…