On the Scattering of a Particle by a Static Potential

DOI10.1103/PhysRev.82.840zbMath0042.45206MaRDI QIDQ5804920

No author found.

Publication date: 1951

Published in: Physical Review (Search for Journal in Brave)

Related Items (94)

Generalization of the Calogero–Cohn bound on the number of bound states ⋮ Titchmarsh–Weyl theory and its relations to scattering theory: Spectral densities and cross sections; Theory and applications ⋮ Effective computation of traces, determinants, and \(\zeta\)-functions for Sturm-Liouville operators ⋮ The inverse resonance problem for Hermite operators ⋮ Trace Formulas for Schrödinger Operators in Connection with Scattering Theory for Finite-gap Backgrounds ⋮ CMV matrices: Five years after ⋮ New estimates on the number of bound states of Schrödinger operators ⋮ A Trace Formula for Differential Operators of Arbitrary Order ⋮ Mandelstam representation for potential scattering ⋮ Upper and lower limits for the number of bound states in a given central potential ⋮ Unnamed Item ⋮ Upper and lower limits for the number of S-wave bound states in an attractive potential ⋮ Honeycomb lattice potentials and Dirac points ⋮ On a mathematical problem encountered in quantum field theory ⋮ Jost functions and determinantal method in potential scattering ⋮ Property of the Vertex Function in Potential Theory ⋮ Dynamical equations and angular momentum ⋮ Some remarks on the renormalization constants and the bound-state condition ⋮ Spectrum of the Scattering Integral Operator in the Physical Energy Sheet ⋮ Singular Potentials and Peratization. I. ⋮ Non-L2 Solutions of Exactly Soluble Relativistic Wave Equations and the Lee Model ⋮ The Jost Function of a Momentum-Dependent Potential ⋮ Sufficient Conditions for an Attractive Potential to Possess Bound States ⋮ Lieb-Thirring type inequality for resonances ⋮ Unnamed Item ⋮ Asymptotic expansions of phase shifts at high energies ⋮ Potential Scattering of High-Energy Electrons in Second Born Approximation ⋮ Born Approximation in a Three-Body Scattering Problem ⋮ Transition from Discrete to Continuous Spectra ⋮ Discretization of inverse scattering on a half line ⋮ Critically shielded potential in a three-dimensional electron gas: The induced charge density at the origin ⋮ Analyticity of the Schrödinger Scattering Amplitude and Nonrelativistic Dispersion Relations ⋮ Dispersion Relations for Dirac Potential Scattering ⋮ The born expansion in non-relativistic quantum theory ⋮ Dispersion relation for potential scattering ⋮ A test of approximation methods in potential scattering ⋮ Theory of Multiple Scattering: Second Born Approximation and Corrections to Molière's Work ⋮ Analytic Properties of Radial Wave Functions ⋮ Upper Bounds on Scattering Lengths for Static Potentials ⋮ Analytic Scattering Theory for Jacobi Operators and Bernstein–Szegö Asymptotics of Orthogonal Polynomials ⋮ Dispersion relations for scattering wave functions in potential theory ⋮ Divergence of the Green's Function Series for Rearrangement Collisions ⋮ Double dispersion relations for deuteron photo- and electrodisintegration ⋮ Recent developments in some non-self-adjoint problems of mathematical physics ⋮ Upper Bounds on Scattering Lengths When Composite Bound States Exist ⋮ Elementary and Composite Particles ⋮ Derivatives of (modified) Fredholm determinants and stability of standing and traveling waves ⋮ Evans functions, Jost functions, and Fredholm determinants ⋮ Variations on a theme of Jost and Pais ⋮ Trace formulas for Schrödinger operators on star graphs ⋮ Spectral \(\zeta\)-functions and \(\zeta\)-regularized functional determinants for regular Sturm-Liouville operators ⋮ Derivation of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>CPT</mml:mi></mml:math>Theorem and the Connection between Spin and Statistics from Postulates of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math>-Matrix Theory ⋮ A sufficient condition for the existence of bound states in a potential ⋮ Weak convergence of spectral shift functions for one‐dimensional Schrödinger operators ⋮ Estimates of 1D resonances in terms of potentials ⋮ A Jost-Pais-type reduction of Fredholm determinants and some applications ⋮ Transition Matrix for Nucleon-Nucleon Scattering. II ⋮ Potential Scattering ⋮ Determinantal Solution of the Fredholm Equation with Green's Function Kernel ⋮ On the numerical evaluation of Fredholm determinants ⋮ Jost functions and Jost solutions for Jacobi matrices. I: A necessary and sufficient condition for Szegő asymptotics ⋮ Applications of the worldline Monte Carlo formalism in quantum mechanics ⋮ Sum rules and spectral measures of Schrödinger operators with \(L^2\) potentials ⋮ Multi-dimensional versions of a determinant formula due to Jost and Pais ⋮ Two-particle scattering theory for anyons ⋮ Complete continuity of kernel in generalized potential scattering. I: Short range interaction without strong singularity. II: Generalized Fourier series expansion ⋮ Continuation and optimization of the Born expansion in nonrelativistic quantum theory ⋮ Equivalence of the effective Hamiltonian approach and the Siegert boundary condition for resonant states ⋮ Bound States in Quantum Field Theory ⋮ Approximation Methods in the Theory of Scattering ⋮ Divergence of Perturbation Theory in Quantum Electrodynamics ⋮ The Validity of Born Expansions ⋮ Bound States and the Interaction Representation ⋮ Construction of a Potential from a Phase Shift ⋮ Eigenvalue Problem in Quantum Electrodynamics ⋮ Absence of embedded eigenvalues for translationally invariant magnetic Laplacians ⋮ The Impulse Approximation ⋮ Fredholm Theory of Scattering in a Given Time-Dependent Field ⋮ Application of Variational Methods to Intermediate and High-Energy Scattering ⋮ Elastic Scattering of Electrons by the Coulomb Field of Nuclei Using Born Approximations ⋮ KdV is well-posed in \(H^{-1}\) ⋮ Perturbation Calculation of the Elastic Scattering of Electrons by Hydrogen Atoms ⋮ On the Convergence of Born Expansions ⋮ Low regularity conservation laws for integrable PDE ⋮ Resonances in one dimension and Fredholm determinants ⋮ Generalized completeness relations in the theory of resonant scattering ⋮ RADIATIVE PHASE TRANSITIONS AND CASIMIR EFFECT INSTABILITIES ⋮ Perturbation of resonances in quantum mechanics ⋮ Existence of Scattering Solutions for the Schrödinger Equation ⋮ Unnamed Item ⋮ Strong Coupling Limit in Potential Theory. I ⋮ Power-Series Expansion of the Unitary Operator<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>U</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi> </mml:mi><mml:mrow><mml:msub><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:math> ⋮ The spectral shift function and Levinson's theorem for quantum star graphs ⋮ Orbital stability of KdV multisolitons in \(H^{-1}\)

Cites Work

This page was built for publication: On the Scattering of a Particle by a Static Potential