Removing cut-offs from one-dimensional Schrodinger operators
- 1 September 1980
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 13 (9) , L295-L298
- https://doi.org/10.1088/0305-4470/13/9/003
Abstract
Deals with the following type of question. Suppose V0(x) is so singular near 0 that the quadratic form of -d2/dx2+V0(x) is unbounded from below, but that (-d2/dx2)D+V0(x) is bounded below where D refers to Dirichlet boundary conditions (BCS) at 0. Let H(a)=-d2/dx2+Va(x) where Va(x) to V0(x) pointwise (AE) as a(spin down)0. Under some additional assumptions on Va, the author proves that H(a) to HD(0) in the norm resolvent sense. Typical for applications is the case where Va are cut-off potentials or regularised potentials of some sort.Keywords
This publication has 1 reference indexed in Scilit:
- On the one-dimensional Coulomb HamiltonianJournal of Physics A: General Physics, 1980