Distribution theory for Schrödinger’s integral equation
From MaRDI portal
Publication:3463245
DOI10.1063/1.4936302zbMath1328.81109arXiv1401.7627OpenAlexW1610161629MaRDI QIDQ3463245
Publication date: 12 January 2016
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1401.7627
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Operations with distributions and generalized functions (46F10) Linear symmetric and selfadjoint operators (unbounded) (47B25) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Topological linear spaces of test functions, distributions and ultradistributions (46F05) Boundary value problems for linear higher-order PDEs (35G15) Time-dependent Schrödinger equations and Dirac equations (35Q41)
Related Items (9)
Conditions for realizing one-point interactions from a multi-layer structure model ⋮ Two-parametric ${\delta'}$ -interactions: approximation by Schrödinger operators with localized rank-two perturbations ⋮ Effects of two successive parity-invariant point interactions on one-dimensional quantum transmission: resonance conditions for the parameter space ⋮ An adjoint-based method for a linear mechanically-coupled tumor model: application to estimate the spatial variation of murine glioma growth based on diffusion weighted magnetic resonance imaging ⋮ Schrödinger operators with singular rank-two perturbations and point interactions ⋮ Bound and scattering states for supersingular potentials ⋮ Regularization of energy-dependent pointlike interactions in 1D quantum mechanics ⋮ Scattering data and bound states of a squeezed double-layer structure ⋮ Families of one-point interactions resulting from the squeezing limit of the sum of two- and three-delta-like potentials
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Bound states and scattering coefficients of the \(-a\delta(x)+b{\delta}'(x)\) potential
- Some remarks on the \(\delta\) '-interaction in one dimension
- Symmetries of Schrödinger operators with point interactions
- Potential theory, path integrals and the Laplacian of the indicator
- A new class of point interactions in one dimension
- Distribution theory for discontinuous test functions and differential operators with generalized coefficients
- Schrödinger operators with \(\delta\) and \(\delta^{\prime}\)-potentials supported on hypersurfaces
- 1D Schrödinger operators with short range interactions: two-scale regularization of distributional potentials
- Boundary conditions for the states with resonant tunnelling across the \(\delta'\)-potential
- A remarkable spectral feature of the Schrödinger Hamiltonian of the harmonic oscillator perturbed by an attractive δ′-interaction centred at the origin: double degeneracy and level crossing
- One-dimensional Schrödinger operators with δ'-interactions on a set of Lebesgue measure zero
- On theS-matrix of Schrödinger operators with non-symmetric zero-range potentials
- Dirac deltas and discontinuous functions
- Resonant tunnelling through short-range singular potentials
- Point interactions of the dipole type defined through a three-parametric power regularization
- On norm resolvent convergence of Schrödinger operators with δ′-like potentials
- Transmission–reflection problem with a potential of the form of the derivative of the delta function
- Explicit time-dependent Schrodinger propagators
- A new class of solvable models in quantum mechanics describing point interactions on the line
- Comments on the Schrodinger equation with delta '-interaction in one dimension
- Contact interactions on graph superlattices
- Generalized point interactions in one-dimensional quantum mechanics
- Time-reversal aspect of the point interactions in one-dimensional quantum mechanics
- Comments on a recent note on the Schrodinger equation with a delta '-interaction
- The regulated four-parameter one-dimensional point interaction
- Proper incorporation of the self-adjoint extension method to the Green function formalism: one-dimensional -function potential case
- On the existence of resonances in the transmission probability for interactions arising from derivatives of Dirac s delta function
- Schrödinger equation with δ' and δ" potentials
- The Fermi pseudo-potential in one dimension
- Four-parameter point-interaction in 1D quantum systems
- Theory and application of Fermi pseudo-potential in one dimension
- Time-dependent propagator with point interaction
- delta '-function perturbations and Neumann boundary conditions by path integration
- Schroedinger operators with (\alpha\delta'+\beta \delta)-like potentials: norm resolvent convergence and solvable models
- Many-body system with a four-parameter family of point interactions in one dimension
- Boundary conditions at the derivative of a delta function
- INTRINSIC RESONANT TUNNELING PROPERTIES OF THE ONE-DIMENSIONAL SCHRÖDINGER OPERATOR WITH A DELTA DERIVATIVE POTENTIAL
- One-dimensional Schrödinger operators with -symmetric zero-range potentials
- Energy-dependent point interactions in one dimension
- A Schrödinger operator with a δ′‐interaction on a Cantor set and Krein–Feller operators
- Scattering properties of point dipole interactions
This page was built for publication: Distribution theory for Schrödinger’s integral equation
