Related papers: A dynamical systems approach to WKB-methods: The e…
This paper deals with eigenvalue optimization problems for a family of natural Schr\"odinger operators arising in some geometrical or physical contexts. These operators, whose potentials are quadratic in curvature, are considered on closed…
The model for Orr--Sommerfeld equation with quadratic profile on the finite interval is considered. The behavior of the spectrum of this problem is completely investigated for large Reynolds numbers. The limit curves are found to which the…
Starting from the Liouville equation, we derive the exact hierarchy of equations satisfied by the reduced distribution functions of the single species point vortex gas in two dimensions. Considering an expansion of the solution in powers of…
For a normalized root system $R$ in $\mathbb R^N$ and a multiplicity function $k\geq 0$ let $\mathbf N=N+\sum_{\alpha \in R} k(\alpha)$. We denote by $dw(\mathbf{x})=\Pi_{\alpha \in R}|\langle \mathbf{x},\alpha…
It is demonstrated that the probability density function, given by the square of a quantum mechanical wavefunction that is a real-valued eigenvector of a time-independent, one-body Schroedinger equation, satisfies a compressible-flow…
We propose an experiential formula for the calculation of the energy eigenvalues of a particle moving in a one-dimension finite-deep square well potential after some physical considerations. This formula shows a simple relation between the…
We study the viscosity solutions to the first eigenvalue equation. We consider $\Omega$ a bounded B-regular domain in $\mathbb{C}^n$ and we prove that the Dirichlet problem $\Lambda_{1}(D_{\mathbb{C}}^2 u)=f$ in $\Omega$ and $u=\varphi$ on…
We consider the eigenvalues and eigenvectors of an axisymmetric matrix$A$ with some special structures. We propose S-Oja-Brockett equation $\frac{dX}{dt}=AXB-XBX^TSAX,$ where $X(t) \in {\mathbb R}^{n \times m}$ with $m \leq n$, $S$ is a…
The single well 1D harmonic oscillator is one of the most fundamental and commonly solved problems in quantum mechanics. Traditionally, in most introductory quantum mechanics textbooks, it is solved using either a power series method, which…
Let $V$ be a {\em periodic} potential on $\RR^3$ that is smooth everywhere except at a discrete set $\maS$ of points, where it has singularities of the form $Z/\rho^2$, with $\rho(x) = |x - p|$ for $x$ close to $p$ and $Z$ is continuous,…
We give a general method to find exact cosmological solutions for scalar-field dark energy in the presence of perfect fluids. We use the existence of invariant transformations for the Wheeler De Witt (WdW) equation. We show that the…
We derive a general form of eigenvalue self-consistency for $GW_{0}$ in the time domain and use it to obtain a simplified postprocessing eigenvalue self-consistency, which we label $\bar{\Delta}GW_{0}$. The method costs the same as a…
An exact quantization rule for the Schr\"{o}dinger equation is presented. In the exact quantization rule, in addition to $N\pi$, there is an integral term, called the quantum correction. For the exactly solvable systems we find that the…
In this note we combine the "spin-argument" from [KLR15] and the $n$-dimensional incompatible, one-well rigidity result from [LL16], in order to infer a new proof for the compactness of discrete multi-well energies associated with the…
We present a class of confining potentials which allow one to reduce the one-dimensional Schroodinger equation to a named equation of mathematical physics, namely either Bessel's or Whittaker's differential equation. In all cases, we…
In this study, we give the variation of parameters method from a different viewpoint for the Nth order inhomogeneous linear ordinary difference equations with constant coefficient by means of delta exponential function . Advantage of this…
We address an eigenvalue problem for the ultrarelativistic (Cauchy) operator $(-\Delta )^{1/2}$, whose action is restricted to functions that vanish beyond the interior of a unit sphere in three spatial dimensions. We provide high accuracy…
In this paper, we present the solutions of the Schr\"{o}dinger equation and the thermodynamic properties of generalized hyperbolic Hulthen and Woods-Saxon potential. The eigenvalues and eigenfunctions were found using the parametric…
The aim of this article is to analyze numerical schemes using two-layer neural networks withinfinite width for the resolution of high-dimensional Schr{\"o}dinger eigenvalue problems with smoothinteraction potentials and Neumann boundary…
This simple text considers an application of Bohr-Sommerfeld quantization rule. It might be of interest for the students of physics.