相关论文: Supersymmetric Method for Constructing Quasi-Exact…
Generalized coherent states for shape invariant potentials are constructed using an algebraic approach based on supersymmetric quantum mechanics. We show this generalized formalism is able to: a) supply the essential requirements necessary…
We study the accuracy of several alternative semiclassical methods by computing analytically the energy levels for many large classes of exactly solvable shape invariant potentials. For these potentials, the ground state energies computed…
The principle of superposition is a key ingredient for quantum mechanics. A recent work [M. Oszmaniec et al., Phys. Rev. Lett. 116, 110403 (2016)] has shown that a quantum adder that deterministically generates a superposition of two…
A new form to construct complex superpotentials that produce real energy spectra in supersymmetric quantum mechanics is presented. This is based on the relation between the nonlinear Ermakov equation and a second order differential equation…
The formalism of Supersymmetric Quantum Mechanics provides us the eigenfunctions to be used in the variational mathod to obtain the eigenvalues for the Hulth\'en Potential.
This paper investigates a novel mechanism for quasi-singularity formation in both linear and nonlinear hyperbolic wave equations in two and three dimensions. We prove that over any finite time interval, there exist inputs such that the…
Although eigenspectra of one dimensional shape invariant potentials with unbroken supersymmetry are easily obtained, this procedure is not applicable when the parameters in these potentials correspond to broken supersymmetry, since there is…
Solving challenging problems in quantum chemistry is one of the most promising applications of quantum computers. Within the quantum algorithms proposed for problems in excited state quantum chemistry, subspace-based quantum algorithms,…
We construct a variety of new exactly-solvable quantum systems, the potentials of which are given in terms of Lambert-W functions. In particular, we generate Schr\"odinger models with energy-dependent potentials, conventional Schr\"odinger…
The accurate quantum chemical calculation of excited states is a challenging task, often requiring computationally demanding methods. When entire ground and excited potential energy surfaces (PESs) are desired, e.g., to predict the…
Full-wave numerical methods based on quasinormal modes (QNMs) offer valuable physical insights and computational efficiency for analyzing electromagnetic resonators. However, despite their advantages, many researchers in electromagnetism…
We present several examples of quasi-exactly solvable $N$-body problems in one, two and higher dimensions. We study various aspects of these problems in some detail. In particular, we show that in some of these examples the corresponding…
The recently proposed PT-symmetric quantum mechanics works with complex potentials which possess, roughly speaking, a symmetric real part and an anti-symmetric imaginary part. We propose and describe a new exactly solvable model of this…
Within the approach of Supersymmetric Quantum Mechanics associated with the variational method a recipe to construct the superpotential of three dimensional confined potentials in general is proposed. To illustrate the construction, the…
A new method for finding electronic structure and wavefunctions of electrons in quasiperiodic potential is introduced. To obtain results it uses slightly modified Schrodinger equation in spaces of dimensionality higher than physical space.…
The quasi-Gaudin algebra was introduced to construct integrable systems which are only quasi-exactly solvable. Using a suitable representation of the quasi-Gaudin algebra, we obtain a class of bosonic models which exhibit this curious…
A method based on supersymmteric (SUSY) quantum mechanics has been developed by exploiting conditional Shape invariance property for obtaining exact ground state solution of generalized polynomial potential with Coulomb term. Specific cases…
A method for a calculation of quantum capacitance for a two-dimesional electron gas (2DEG) in potential wells of complicated geometry on the base of a quantum wave impedance technique was proposed. The application of this method was…
New solutions for second-order intertwining relations in two-dimensional SUSY QM are found via the repeated use of the first order supersymmetrical transformations with intermediate constant unitary rotation. Potentials obtained by this…
It is known that the spectrum of quasi-normal modes of potential barriers is related to the spectrum of bound states of the corresponding potential wells. This property has been widely used to compute black hole quasi-normal modes, but it…