Related papers: Self-adjoint extension for Maxwell-Chern-Simons mo…

In this paper, we examine eigenfunctions of a generalized Landau Magnetic Laplacian that models the physics of an electron confined to a plane in a magnetic field orthogonal to the plane. This operator has an infinite dimensional null space…

We study a Klein-Gordon-Maxwell system, in a bounded spatial domain, under Neumann boundary conditions on the electric potential. We allow a nonconstant coupling coefficient. For sufficiently small data, we find infinitely many standing…

The self-adjoint extension (SAE) procedure is considered in the Schrodinger equation for potentials behaving as an attractive inverse square at the origin of coordinates. This approach guarantees self-adjointness of the radial Hamiltonian…

The main objective of this dissertation is to analyse thoroughly the construction of self-adjoint extensions of the Laplace-Beltrami operator defined on a compact Riemannian manifold with boundary and the role that quadratic forms play to…

We show that the boundary conditions entering in the definition of the self-adjoint operator describing the Laplacian plus a finite number of point interactions are local if and only if the corresponding wave equation has finite speed of…

The momentum-dependent local-ansatz (MLA) wavefunction describes well correlated electrons in solids in both the weak and strong interaction regimes. In order to apply the theory to the realistic system, we have extended the MLA to the…

Landau and Lifshitz [4, Section 35] conjectured that for an arbitrary $k\in \mathbb{R}$, there exists the motion of a quantum mechanical particle under the inverse square potential $k|x|^{-2}$, $x \in \mathbb{R}^3$. When $k$ is negative and…

We develop the concept of operators in Hilbert spaces which are similar to their adjoints via antiunitary operators, the latter being not necessarily involutive. We discuss extension theory, refined polar and singular-value decompositions,…

We present a large-$N$ collective field formalism for anyons in external magnetic fields interacting with arbitrary two-body potential. We discuss how the Landau level is reproduced in our framework. We apply it to the soluble model for…

We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended…

The Aharonov-Casher problem in the presence of a Lorentz-violating background nonminimally coupled to a spinor and a gauge field is examined. Using an approach based on the self-adjoint extension method, an expression for the bound state…

A large time expansion for the propagator associated to a semiclassical non-selfadjoint magnetic Schr\"odinger operator is established, in terms of the low lying eigenvalues of the operator.

One-dimensional $\delta^{'}$-function potential is discussed in the framework of Green's function formalism without invoking perturbation expansion. It is shown that the energy-dependent Green's function for this case is crucially dependent…

The structure of deformed single-particle wave functions in the vicinity of zero energy limit is studied using a schematic model with a quadrupole deformed finite square-well potential. For this purpose, we expand the single-particle wave…

The matrix Schroedinger equation with a selfadjoint matrix potential is considered on the half line with the general selfadjoint boundary condition at the origin. When the matrix potential is integrable, the high-energy asymptotics are…

We study a class of self-adjoint operators defined on the direct sum of two Hilbert spaces: a finite dimensional one called sometimes a ``small subsystem'' and an infinite dimensional one -- a ``reservoir''. The operator, which we call a…

We consider the quantum mechanics of an electron trapped on an infinite band along the $x$-axis in the presence of the Morse-like perpendicular magnetic field $\vec{B}=-B_{0}e^{-\frac{2\pi}{a_{0}}x}\hat{k}$ with $B_{0}>0$ as a constant…

We consider the AdS/CFT correspondence for theories with a Chern-Simons term in three dimensions. We find the two-point functions of the boundary conformal field theories for the Proca-Chern-Simons theory and the Self-Dual model. We also…

We prove the Schr\"odinger operator with infinitely many point interactions in $\mathbb{R}^d$ $(d=1,2,3)$ is self-adjoint if the support of the interactions is decomposed into uniformly discrete clusters. Using this fact, we prove the…

We consider the Laplace operator with Dirichlet boundary conditions on a planar domain and study the effect that performing a scaling in one direction has on the spectrum. We derive the asymptotic expansion for the eigenvalues and…