相关论文: Upper and lower bounds for an eigenvalue associate…

Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a…

The eigenvalue problem for one-dimensional Schr\"{o}dinger equation with the rational potential is numerically solved by the operator method. We show that the operator method, applied for solving the Schr\"{o}dinger equation with the…

This paper is devoted to the construction of what we will call {\em exactly solvable models}, i.e. of quantum mechanical systems described by an Hamiltonian $H$ whose eigenvalues and eigenvectors can be explicitly constructed out of some…

In this paper, we investigate the behavior of the eigenvalues of a magnetic Aharonov-Bohm operator with half-integer circulation and Dirichlet boundary conditions in a bounded planar domain. We establish a sharp relation between the rate of…

We prove essential self-adjointness for semi-bounded below magnetic Schr\"odinger operators on complete Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. Some singularities of the scalar…

We consider a nonlinear eigenvalue problem under Robin boundary conditions in a domain with (possibly noncompact) smooth boundary. The problem involves a weighted p-Laplacian operator and subcritical nonlinearities satisfying…

We review various attempts to localize the discrete spectra of semirelativistic Hamiltonians of the form H = \beta \sqrt{m^2 + p^2} + V(r) (w.l.o.g. in three spatial dimensions) as entering, for instance, in the spinless Salpeter equation.…

For a very general class of unbounded self-adjoint operator function we prove upper bounds for eigenvalues which lie within arbitrary gaps of the essential spectrum. These upper bounds are given by triple variations. Furthermore, we find…

Two-sided estimates for higher order eigenvalues are presented for a class of non-local Schr\"odinger operators by using the jump rate and the growth of the potential. For instance, let $L$ be the generator of a L\'evy process with L\'evy…

Our main result is a theorem saying that a bounded operator $A$ on a Hilbert space belongs to a certain set associated with its self-commutator $[A^*,A]$, provided that $A-zI$ can be approximated by invertible operators for all complex…

Eigenvalue behaviors of Schr\"odinger operator defined on $n$-dimensional lattice with $n+1$ delta potentials is studied. It can be shown that lower threshold eigenvalue and lower threshold resonance are appeared for $n\geq 2$, and lower…

Bound states of hyperbolic potential is investigated by means of a generalized pseudospectral method. Significantly improved eigenvalues, eigenfunctions are obtained efficiently for arbitrary $n, \ell$ quantum states by solving the relevant…

The spinless Salpeter equation may be considered either as a standard approximation to the Bethe--Salpeter formalism, designed for the description of bound states within a relativistic quantum field theory, or as the most simple, to a…

We prove that the eigenvalues of a continuum random Schr\"odinger operator $-\Delta+ V_{\omega}$ of Anderson type, with complex decaying potential, can be bounded (with high probability) in terms of an $L^q$ norm of the potential for all…

Schr\"odinger operator on half-line with complex potential and the corresponding evolution are studied within perturbation theoretic approach. The total number of eigenvalues and spectral singularities is effectively evaluated. Wave…

Let $\Omega$ be a bounded domain in $\mathbb R^2$ with smooth boundary $\partial\Omega$, and let $\omega_h$ be the set of points in $\Omega$ whose distance from the boundary is smaller than $h$. We prove that the eigenvalues of the…

This paper gives a framework to produce the lower bound of eigenvalues defined in a Hilbert space by the eigenvalues defined in another Hilbert space. The method is based on using the max-min principle for the eigenvalue problems.

We study solutions of the functional eigenstate equation of a free quantum field Hamiltonian. Admissible solutions are to have a finite norm and a finite eigenvalue w.r.t. the norm and eigenvalue of the ground state of the free theory. We…

We study the Schr\"odinger operator with a potential given by the sum of the potentials for harmonic oscillator and imaginary cubic oscillator and we focus on its pseudospectral properties. A summary of known results about the operator and…

We consider the magnetic Steklov eigenvalue problem on compact Riemannian manifolds with boundary for generic magnetic potentials and establish various results concerning the spectrum. We provide equivalent characterizations of magnetic…