Related papers: 1D Schr\"odinger operators with complex potentials

We consider Schr\"odinger operators with complex-valued decreasing potentials on the half-line. Such operator has essential spectrum on the half-line plus eigenvalues (counted with algebraic multiplicity) in the complex plane without the…

We consider Schr\"odinger operators with complex decaying potentials (in general, not from trace class) on the lattice. We determine trace formulae and estimate of eigenvalues and singular measure in terms of potentials. The proof is based…

We consider 3-dim Schr\"odinger operators with a complex potential. We obtain new trace formulas. In order to prove these results we study analytic properties of a modified Fredholm determinant. In fact we reformulate spectral theory…

We study the eigenvalues of Schr\"odinger operators with complex potentials in odd space dimensions. We obtain bounds on the total number of eigenvalues in the case where $V$ decays exponentially at infinity.

We establish quantitative upper and lower bounds for Schr\"odinger operators with complex potentials that satisfy some weak form of sparsity. Our first result is a quantitative version of an example, due to S.\ Boegli (Comm. Math. Phys.,…

Several aspects of complex-valued potentials generating a real and positive spectrum are discussed. In particular, we construct complex-valued potentials whose corresponding Schr\"odinger eigenvalue problem can be solved analytically.

We consider Schr\"odinger operators with periodic potentials in the positive quadrant for dim $>1$ with Dirichlet boundary condition. We show that for any integer $N$ and any interval $I$ there exists a periodic potential such that the…

We consider a Sturm-Liouville operator a with integrable potential $q$ on the unit interval $I=[0,1]$. We consider a Schr\"odinger operator with a real compactly supported potential on the half line and on the line, where this potential…

Estimates for eigenvalues of Schr\"{o}dinger operators on the half-line with complex-valued potentials are established. Schr\"{o}dinger operators with potentials belonging to weak Lebesque's classes are also considered. The results cover…

The aim of this paper is to provide uniform estimates for the eigenvalue spacings of one-dimensional semiclassical Schr\"odinger operators with singular potentials on the half-line. We introduce a new development of semiclassical measures…

We consider Schr\"odinger operators in $\mathbb R^d$ with complex potentials supported on a hyperplane and show that all eigenvalues lie in a disk in the complex plane with radius bounded in terms of the $L^p$ norm of the potential with…

We study the Schr\"odinger operator with a potential given by the sum of the potentials for harmonic oscillator and imaginary cubic oscillator and we focus on its pseudospectral properties. A summary of known results about the operator and…

We derive a sharp bound on the location of non-positive eigenvalues of Schroedinger operators on the halfline with complex-valued potentials.

We study singular Schr\"odinger operators on a finite interval as selfadjoint extensions of a symmetric operator. We give sufficient conditions for the symmetric operator to be in the $n$-entire class, which was defined in our previous…

An explicit construction is provided for embedding n positive eigenvalues in the spectrum of a Schroedinger operator on the half-line with a Dirichlet boundary condition at the origin. The resulting potential is of von Neumann-Wigner type,…

Estimates for the total multiplicity of eigenvalues for Schr\"odinger operator are established in the case of compactly supported or exponentially decreasing complex-valued potential.

Inequalities are derived for power sums of the real part and the modulus of the eigenvalues of a Schr\"odinger operator with a complex-valued potential.

We study one-dimensional Schr\"{o}dinger operators $\mathrm{S}(q)$ on the space $L^{2}(\mathbb{R})$ with potentials $q$ being complex-valued generalized functions from the negative space $H_{unif}^{-1}(\mathbb{R})$. Particularly the class…

Let P be the operator $-\Delta+V$ on R^d, where $V$ is a real potential with several inverse square singularities. The usual non-trapping type high-frequency inequality on the truncated resolvent of $P$ is shown, using semi-classical…

Using an extension of the H\"ormander product of distributions, we obtain an intrinsic formulation of one-dimensional Schr\"odinger operators with singular potentials. This formulation is entirely defined in terms of standard {\it Schwartz}…