Related papers: Gordon type Theorem for measure perturbation
In this paper, we generalize some halfspace type theorems for self-shrinkers of codimension 1 to the case of arbitrary codimension.
We introduce a new, more general type of nonlinear gauge transformation in nonrelativistic quantum mechanics that involves derivatives of the wave function and belongs to the class of B\"acklund transformations. These transformations…
In modified theories of gravity, the potentials appearing in the Schr\"odinger-like equations that describe perturbations of non-rotating black holes are also modified. In this paper we ask: can these modifications be constrained with…
An analogue of Rellich's theorem is proved for discrete Laplacian on square lattice, and applied to show unique continuation property on certain domains as well as non-existence of embedded eigenvalues for discrete Schr{\"o}dinger…
We use an observation of Bohr connecting Dirichlet series in the right half plane $\mathbb{C}_+$ to power series on the polydisk to interpret Carlson's theorem about integrals in the mean as a special case of the ergodic theorem by…
We present here a systematic and unified treatment to connect the Schrodinger equation corresponding to generalized Morse and Poschl-Teller potentials. We then show that the wave functions and generalized potentials are linked through the…
A theorem that relies only on the unitary property of the Schroedinger equation and not upon any classical or semi-classical approximation negates some, but not all, suggestions that have been made for measuring the neutron's…
A variational method is discussed, extending the Gaussian effective potential to higher orders. The single variational parameter is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the…
We give an explicit axiomatic formulation of the quantum measurement theory which is free of the projection postulate. It is based on the generalized nondemolition principle applicable also to the unsharp, continuous-spectrum and…
We propose a new integral based on Taylor measures, study its properties extensively, and we illustrate that it includes many concepts from mathematics as special cases. In particular, the new integral emerges as a generalization of the…
A simple proof of Egorov's theorem for infinite measure is given
We prove a Wegner estimate for discrete Schr\"odinger operators with a potential given by a Gaussian random process. The only assumption is that the covariance function decays exponentially, no monotonicity assumption is required. This…
We analyze dynamical properties of the logarithmic Schr{\"o}dinger equation under a quadratic potential. The sign of the nonlinearity is such that it is known that in the absence of external potential, every solution is dispersive, with a…
We prove uniform resolvent estimates for an abstract operator given by a dissipative perturbation of a self-adjoint operator in the sense of forms. For this we adapt the commutators method of Mourre. We also obtain the limiting absorption…
We consider a quantum particle in a 1D interval submitted to a potential. The evolution of this particle is controlled using an external electric field. Taking into account the so-called polarizability term in the model (quadratic with…
We reformulate the theory of Schwarzschild black hole perturbations in terms of the metric perturbation in the Lorenz gauge. In this formulation, each tensor-harmonic mode of the perturbation is constructed algebraically from 10 scalar…
We establish a Schur--Horn type inequality for symmetric hyperbolic polynomials. As an immediate consequence, we resolve a conjecture of Nam Q. Le on Hadamard-type inequalities for hyperbolic polynomials. Our argument is based on the…
We show explicitly that the question of gauge invariance of the effective potential in standard scalar electrodynamics remains unchanged despite the introduction of the Chern-Simons term. The result does not depend on the presence of the…
There is considered an extension of gauge theories according to the assumption of a generalized uncertainty principle which implies a minimal length scale. A modification of the usual uncertainty principle implies an extended shape of…
Original English Summary. - A systematic method of constructing potentials, for which the one-variable Schroedinger equation can be solved in terms of the hypergeometric (HGM) function, is presented. All the potentials, obtained by…