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Singular continuous spectrum of one-dimensional Schrödinger operator with point interactions on a sparse set
Singular continuous spectrum one-dimensional Schrö dinger operator
2010/11/18
We say that a discrete set $X =\{x_n\}_{n\in\dN_0}$ on the half-line $$0=x_0 < x_1 infty$$ is sparse in the case the distances $\Delta x_n = x_{n+1} -x_n$ between neighboring p...
Spectral Singularities, Biorthonormal Systems, and a Two-Parameter Family of Complex Point Interactions
complex potential spectral singularity biorthonormal system scattering bound state quasi-Hermitian PT -symmetry point interaction
2010/4/13
A curious feature of complex scattering potentials v(x) is the appearance of spectral singularities. We offer a quantitative description of spectral singularities that identifies them with an obstruct...
A Remark on One-Dimensional Many-Body Problems with Point Interactions
Remark One-Dimensional Many-Body Problems Point Interactions
2010/10/15
The integrability of one dimensional quantum mechanical many-body problems with general contact interactions is extensively studied. It is shown that besides the pure (repulsive or attractive) δ-funct...