相关论文: On the self-adjointness of H+A*+A

We examine a new application of the Holstein-Primakoff realization of the simple harmonic oscillator Hamiltonian. This involves the use of infinite-dimensional representations of the Lie algebra $su(2)$. The representations contain…

Let $A$ be a self-adjoint operator on a Hilbert space $\fH$. Assume that the spectrum of $A$ consists of two disjoint components $\sigma_0$ and $\sigma_1$ such that the convex hull of the set $\sigma_0$ does not intersect the set…

We study $H=D^*D+V$, where $D$ is a first order elliptic differential operator acting on sections of a Hermitian vector bundle over a Riemannian manifold $M$, and $V$ is a Hermitian bundle endomorphism. In the case when $M$ is geodesically…

The purely algebraic technique associated with the creation and annihilation operators to resolve the radial equation of Hydrogen-like atoms (HLA) for generating the bound energy spectrum and the corresponding wave functions is suitable for…

For a purely imaginary sign-definite perturbation of a self-adjoint operator, we obtain exponential representations for the perturbation determinant in both upper and lower half-planes and derive respective trace formulas.

In this paper, we consider self-adjoint difference equations of the form -\Delta(a_{n-1}\Delta y_{n-1})+b_{n}y_{n}=\lambda y_{n},n=0,1,...\label{eq:abstract} where $a_{n-1}>0$ for all $n\ge0$ and $b_{n}$ are real and $\lambda$ is complex.…

It is well known that in the commutative case, i.e. for $A=C(X)$ being a commutative C*-algebra, compact selfadjoint operators acting on the Hilbert C*-module $H_A$ (= continuous families of such operators $K(x)$, $x\in X$) can be…

We consider the discrete one-dimensional Schr\"{o}dinger operator $H=H_0+V$, where $(H_0x)[n]=-(x[n+1]+x[n-1]-2x[n])$ and $V$ is a self-adjoint operator on $\ell^2(\mathbb{Z})$ with a decay property given by $V$ extending to a compact…

In the recent years a generalization $H=p^2 +x^2(ix)^\epsilon$ of the harmonic oscillator using a complex deformation was investigated, where \epsilon\ is a real parameter. Here, we will consider the most simple case: \epsilon even and x…

For a von Neumann algebra M acting on a Hilbert space H with a cyclic and separating vector v, we investigate the structure of Dirichlet forms on the natural standard form associated with the pair (M,v). For a general Lindblad type…

We prove operator-norm resolvent convergence estimates for one-dimensional periodic differential operators with rapidly oscillating coefficients in the non-uniformly elliptic high-contrast setting, which has been out of reach of the…

Through the Kre\u{\i}n-Vi\v{s}ik-Birman extension scheme, unlike the classical analysis based on von Neumann's theory, we reproduce the construction and classification of all self-adjoint realisations of three-dimensional hydrogenoid-like…

In this paper we continue studying of matrix $n\times n$ linear differential intertwining operators. The problems of minimization and of reducibility of matrix intertwining operators are considered and criterions of weak minimizability and…

The recently introduced two- and three-parameter ($p,q$)- and ($p,q,\mu$)-deformed extensions of the Heisenberg algebra were explored under the condition of their connectedness with the respective nonstandard (other than known ones)…

This monograph contains revised and enlarged materials from previous lecture notes of undergraduate and graduate courses and seminars delivered by both authors over the last years on a subject that is central both in abstract operator…

Let $\mathbf{A}$ be a bounded self-adjoint operator on a separable Hilbert space $\mathfrak{H}$ and $\mathfrak{H}_0\subset\mathfrak{H}$ a closed invariant subspace of $\mathbf{A}$. Assuming that $\sup\spec(A_0)\leq \inf\spec(A_1)$, where…

We consider the Hamiltonian $H$ of a 3D spinless non-relativistic quantum particle subject to parallel constant magnetic and non-constant electric field. The operator $H$ has infinitely many eigenvalues of infinite multiplicity embedded in…

We show that a simplified version of the Dirac interaction operator given by $\hat H_\mathrm{I} \propto \int d\mathbf{k}d\mathbf{p}(\hat a(\mathbf{k}) + \hat a^\dagger(-\mathbf{k})) \hat b^\dagger(\mathbf{p} + \mathbf{k}) \hat…

A unified S-matrix framework of quantum singular interactions is presented for the comparison of self-adjoint extensions and physical renormalization. For the long-range conformal interaction the two methods are not equivalent, with…

Let S be a symmetric relation with deficiency index (1,1). In this article, we extend Krein`s resolvent formalism in order to describe all, not necessarily self-adjoint, extensions $S \subset \tilde{A}$ with $\varrho(\tilde{A})\neq…