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Let $A$ be a symmetric operator. By using the method of boundary triplets we parameterize in terms of a Nevanlinna parameter $\tau$ all exit space extensions $\wt A=\wt A^*$ of $A$ with the discrete spectrum $\s(\wt A)$ and characterize the…
In this note, we study the potential algebra for several models arising out of quantum mechanics with generalized uncertainty principle. We first show that the eigenvalue equation corresponding to the momentum-space Hamiltonian…
The spectral properties of the singularly perturbed self-adjoint Landau Hamiltonian $A_\alpha =(i \nabla + A)^2 + \alpha\delta$ in $L^2(R^2)$ with a $\delta$-potential supported on a finite $C^{1,1}$-smooth curve $\Sigma$ are studied. Here…
We derive the so-called first law of black hole mechanics for variations about stationary black hole solutions to the Einstein--Maxwell equations in the absence of sources. That is, we prove that $\delta M=\kappa\delta A+\omega\delta J+VdQ$…
We study the problem originally communicated by E. Meckes on the asymptotics for the eigenvalues of the kernel of the unitary eigenvalue process of a random $n \times n$ matrix. The eigenvalues $p_{j}$ of the kernel are, in turn, associated…
Based on the novel prescription for the power of a complex number, a new expression for the eigenfunction of the operator of the third component of the angular momentum is presented. These functions are normalizable, single valued and are…
In this paper, we propose a new finite element approach, which is different than the classic Babuska-Osborn theory, to approximate Dirichlet eigenvalues. The Dirichlet eigenvalue problem is formulated as the eigenvalue problem of a…
Motivated by the uniqueness problem for monostable semi-wavefronts, we propose a revised version of the Diekmann and Kaper theory of a nonlinear convolution equation. Our version of the Diekmann-Kaper theory allows 1) to consider new types…
We establish $C^{1,1}$-regularity and uniqueness of the first eigenfunction of the complex Hessian operator on strongly $m$-pseudoconvex manifolds, along with a variational formula for the first eigenvalue. From these results, we derive a…
Relativity and quantum mechanics are generalized by considering a finite limit for the smallest measurable distance. The value a of this quantum of length is unknown, but it is a universal constant, like c and h. It depends on the total…
We describe a highly efficient numerical scheme for finding two-sided bounds for the eigenvalues of the fractional Laplace operator (-Delta)^{alpha/2} in the unit ball D in R^d, with a Dirichlet condition in the complement of D. The…
This paper concerns the eigenvalues of the Neumann-Poincar\'e operator, a boundary integral operator associated with the harmonic double-layer potential. Specifically, we examine how the eigenvalues depend on the support of integration and…
We study the stationary problem of a charged Dirac particle in (2+1) dimensions in the presence of a uniform magnetic field B and a singular magnetic tube of flux Phi = 2 pi kappa/e. The rotational invariance of this configuration implies…
Following the semiclassical formalism of Strutinsky et al., we have obtained the complete eigenvalue spectrum for a particle enclosed in an infinitely high spheroidal cavity. Our spheroidal trace formula also reproduces the results of a…
In this paper we are interested in the following fourth order eigenvalue problem coming from the buckling of thin films on liquid substrates: \begin{equation*} \begin{cases} \Delta^2 u+ \kappa^2 u=-\lambda \Delta u &\text{in } B_1,\newline…
We study spectral properties of Dirac operators on bounded domains $\Omega \subset \mathbb{R}^3$ with boundary conditions of electrostatic and Lorentz scalar type and which depend on a parameter $\tau\in\mathbb{R}$; the case $\tau = 0$…
In this paper, we analyze an eigenvalue problem for quasi-linear elliptic operators involving homogeneous Dirichlet boundary conditions in a open smooth bounded domain. We show that the eigenfunctions corresponding to the eigenvalues belong…
We prove that the linear delta expansion for energy eigenvalues of the quantum mechanical anharmonic oscillator converges to the exact answer if the order dependent trial frequency $\Omega$ is chosen to scale with the order as…
In the present paper we consider a family of $2 \times 2$ operator matrices ${\mathcal A}_\mu(k),$ $k \in {\Bbb T}^3:=(-\pi, \pi]^3,$ $\mu>0,$ associated with the Hamiltonian of a system consisting of at most two particles on a…
In this paper we consider eigenvalues asymptotics of the energy operator in the one of the most interesting models of quantum physics, describing an interaction between two-level system and harmonic oscillator. The energy operator of this…