Add to ORKGIn this thesis I look at the theory of compact operators in a general Hilbert space, as well as the inverse of the Hamiltonian operator in the specific case of L2[a,b]. I show that this inverse is a compact, positive, and bounded linear operator. Also the eigenfunctions of this operator form a basis for the space of continuous functions as a subspace of L2[a,b]. A numerical method is proposed to solve for these eigenfunctions when the Hamiltonian is considered as an operator on R n. The paper finishes with a discussion of examples of Schrödinger equations and the solutions
AbstractWe study the asymptotic behavior, in a “semi-classical limit,” of the first eigenvalues (i.e...
AbstractWe investigate the rate of decay of eigenfunctions of Schrödinger equations using a perturba...
AbstractConsider the operator equation, AX − XB = Q(∗), in which A, B, Q are appropriately given bou...
In this thesis I look at the theory of compact operators in a general Hilbert space, as well as the ...
In this article, we investigate the discreteness and some other properties of the spectrum for the S...
We consider Schrödinger operators H = −1/2 Δ + V for a large class of potentials. V. We show that if...
We provide an exact version of the Egorov Theorem for a class of Schrödinger operators in 2(), where...
AbstractWe consider Schrödinger operators H = − 12Δ + V for a large class of potentials. V. We show ...
AbstractWe treat the Schrödinger operator A=−Δ+q(x)• on L2(RN) with the potential q:RN→[q0,∞) bounde...
The main purpose of this paper is to extend some theory of Schrödinger operators from one dimension ...
International audienceWe determine the Schatten class for the compact resolvent of Dirichlet realiza...
AbstractWe study the nonlinear problem −Δu+V(x)=f(x,u), x∈RN, lim|x|→∞u(x)=0, where the Schrödinger ...
We develop linear and nonlinear harmonic analysis on compact Lie groups and homogeneous spaces relev...
AbstractAn L-basis associated to a linear second-order ordinary differential operator L is an infini...
Abstract. In this paper we study rigorous spectral theory and solvability for both the direct and in...
AbstractWe study the asymptotic behavior, in a “semi-classical limit,” of the first eigenvalues (i.e...
AbstractWe investigate the rate of decay of eigenfunctions of Schrödinger equations using a perturba...
AbstractConsider the operator equation, AX − XB = Q(∗), in which A, B, Q are appropriately given bou...
In this thesis I look at the theory of compact operators in a general Hilbert space, as well as the ...
In this article, we investigate the discreteness and some other properties of the spectrum for the S...
We consider Schrödinger operators H = −1/2 Δ + V for a large class of potentials. V. We show that if...
We provide an exact version of the Egorov Theorem for a class of Schrödinger operators in 2(), where...
AbstractWe consider Schrödinger operators H = − 12Δ + V for a large class of potentials. V. We show ...
AbstractWe treat the Schrödinger operator A=−Δ+q(x)• on L2(RN) with the potential q:RN→[q0,∞) bounde...
The main purpose of this paper is to extend some theory of Schrödinger operators from one dimension ...
International audienceWe determine the Schatten class for the compact resolvent of Dirichlet realiza...
AbstractWe study the nonlinear problem −Δu+V(x)=f(x,u), x∈RN, lim|x|→∞u(x)=0, where the Schrödinger ...
We develop linear and nonlinear harmonic analysis on compact Lie groups and homogeneous spaces relev...
AbstractAn L-basis associated to a linear second-order ordinary differential operator L is an infini...
Abstract. In this paper we study rigorous spectral theory and solvability for both the direct and in...
AbstractWe study the asymptotic behavior, in a “semi-classical limit,” of the first eigenvalues (i.e...
AbstractWe investigate the rate of decay of eigenfunctions of Schrödinger equations using a perturba...
AbstractConsider the operator equation, AX − XB = Q(∗), in which A, B, Q are appropriately given bou...