12 citations · 20 across the 8 of their papers we have counts for
6 papers · 1 filter
An improved bound for the ground state of a Schrödinger operator on a loop
Helmut Linde
Consider a closed curve of length with curvature and the Schrödinger operator with as the potential term. Let be the lowest eigenvalue of . The Ovals…
Geometrically induced two-particle binding in a wave guide
Helmut Linde
For mathematical models of quantum wave guides we show that in some situations two interacting particles can be trapped more easily than a single particle. In particular, we give a…
A second eigenvalue bound for the Dirichlet Laplacian in hyperbolic space
Rafael D. Benguria, Helmut Linde
Let be some domain in the hyperbolic space $\Hn$ (with ) and the geodesic ball that has the same first Dirichlet eigenvalue as . We prove the Payne-Pólya-Weinb…
A second eigenvalue bound for the Dirichlet Schroedinger operator
Rafael D. Benguria, Helmut Linde
Let be the th eigenvalue of the Schrödinger operator with Dirichlet boundary conditions on a bounded domain and with the positive potential . Follo…
Quantitative estimates on the enhanced binding for the Pauli-Fierz operator
Jean-Marie Barbaroux, Helmut Linde, Semjon Vugalter
For a quantum particle interacting with a short-range potential, we estimate from below the shift of its binding threshold, which is due to the particle interaction with a quantize…
A lower bound for the ground state energy of a Schroedinger operator on a loop
Helmut Linde
Consider a one dimensional quantum mechanical particle described by the Schroedinger equation on a closed curve of length . Assume that the potential is given by the square of…