Results 1 to 10 of about 73,171 (204)
Area Distribution of Elastic Brownian Motion
, 2009 We calculate the excursion and meander area distributions of the elastic Brownian motion by using the self adjoint extension of the Hamiltonian of the free quantum particle on the half line.
Albeverio S +8 more
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Degenerate elliptic operators in one dimension [PDF]
, 2009 Let $H$ be the symmetric second-order differential operator on $L_2(\Ri)$ with domain $C_c^\infty(\Ri)$ and action $H\varphi=-(c \varphi')'$ where $ c\in W^{1,2}_{\rm loc}(\Ri)$ is a real function which is strictly positive on $\Ri\backslash\{0\}$ but ...
Robinson, Derek W., Sikora, Adam
core +2 more sources
Fall to the centre in atom traps and point-particle EFT for absorptive systems
Journal of High Energy Physics, 2018 Polarizable atoms interacting with a charged wire do so through an inverse-square potential, V = −g/r 2. This system is known to realize scale invariance in a nontrivial way and to be subject to ambiguities associated with the choice of boundary ...
R. Plestid +2 more
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Point-particle effective field theory I: classical renormalization and the inverse-square potential
Journal of High Energy Physics, 2017 Singular potentials (the inverse-square potential, for example) arise in many situations and their quantum treatment leads to well-known ambiguities in choosing boundary conditions for the wave-function at the position of the potential’s singularity ...
C.P. Burgess +3 more
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Adjoint and self-adjoint differential operators on graphs
Electronic Journal of Differential Equations, 1998 A differential operator on a directed graph with weighted edges is characterized as a system of ordinary differential operators. A class of local operators is introduced to clarify which operators should be considered as defined on the graph.
Robert Carlson
doaj
Frontiers in Physics, 2019 We consider singular self-adjoint extensions for the Schrödinger operator of spin-1/2 particle in one dimension. The corresponding boundary conditions at a singular point are obtained. There are boundary conditions with the spin-flip mechanism, i.e., for
Vladimi L. Kulinskii +2 more
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Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2020 A nonlinear two-dimensional orthotropic filtration equation with the Riemann–Liouville time-fractional derivative is considered. It is proved that this equation can admits only linear autonomous groups of point transformations.
Veronika Olegovna Lukashchuk +1 more
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On spectral stability for rank one singular perturbations [PDF]
Opuscula MathematicaWe study the embedded point spectrum of rank one singular perturbations of an arbitrary self-adjoint operator \(A\) on a Hilbert space \(\mathcal{H}\). These perturbations can be regarded as self-adjoint extensions of a densely defined closed symmetric ...
Mario Alberto Ruiz Caballero +1 more
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Electronic Journal of Differential Equations, 2005 Two different self-adjoint Pauli extensions describing a spin-1/2 two-dimensional quantum system with singular magnetic field are studied. An Aharonov-Casher type formula is proved for the maximal Pauli extension and the possibility of approximation of ...
Mikael Persson
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Planar density of vacuum charge induced by a supercritical Coulomb potential
Physics Letters B, 2017 Analytical expressions for the planar density of an induced vacuum charge are obtained in a strong Coulomb potential in coordinate space. Treatment is based on a self-adjoint extension approach for constructing of the Green's function of a charged ...
V.R. Khalilov, I.V. Mamsurov
doaj +1 more source