New shape-invariant potentials in supersymmetric quantum mechanics

A New Solvable Generalized Trigonometric Tangent Potential Based on SUSYQM

Supersymmetric quantum mechanics has wide applications in physics. However, there are few potentials that can be solved exactly by supersymmetric quantum mechanics methods, so it is undoubtedly of great significance to find more potentials that can be solved exactly. This paper studies the supersymmetric quantum mechanics problems of the Schrödinger equation with a new kind of generalized trigonometric tangent superpotential: Atannpx+Btanmpx. We will elaborate on this new potential in the following aspects. Firstly, the shape invariant relation of partner potential is generated by the generalized trigonometric tangent superpotential. We find three shape invariance forms that satisfy the additive condition. Secondly, the eigenvalues and the eigenwave functions of the potential are studied separately in these three cases. Thirdly, the potential algebra of such a superpotential is discussed, and the discussions are explored from two aspects: one parameter’s and two parameters’ potential algebra. Through the potential algebra, the eigenvalue spectrums are given separately which are consistent with those mentioned earlier. Finally, we summarize the paper and give an outlook on the two-parameter shape-invariant potential.

Classes of Balanced Gain-and-Loss Waveguides as Non-Hermtian Potential Hierarchies

In this work, we report the construction of different classes of complex-valued refractive index landscapes, with real spectra, in the framework of the factorization method. The particular case of guiding hyperbolic-type profiles is considered in the PT- and non-PT-symmetric configurations. In both schemes, the imaginary part of the refractive index satisfies the zero-total-area condition indicating that the total transverse optical power is preserved, allowing stable propagating modes to be obtained. The spectra and the guided modal field amplitudes are obtained and their orthogonality relations are established.