On the number of bound states for the one-dimensional Schrödinger equation

DOI10.1063/1.532510zbMath0931.34069OpenAlexW2056401843MaRDI QIDQ4701647

Tuncay Aktosun, Martin Klaus, Cornelis V. M. van der Mee

Publication date: 21 November 1999

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10919/47072

zbMATH Keywords

bound statesone-dimensional Schrödinger equation

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05)

Related Items (11)

Spectrum of periodic elliptic operators with distant perturbations in space ⋮ Upper and lower limits for the number of S-wave bound states in an attractive potential ⋮ Nonlinear Schrödinger equations with exceptional potentials ⋮ On occurrence of resonances from multiple eigenvalues of the Schrödinger operator in a cylinder with distant perturbations ⋮ Factorization and small-energy asymptotics for the radial Schrödinger equation ⋮ On finitely many resonances emerging under distant perturbations in multi-dimensional cylinders ⋮ Inverse scattering with partial information on the potential ⋮ A single-mode quantum transport in serial-structure geometric scatterers ⋮ Computational methods for some inverse scattering problems ⋮ On infinite system of resonance and eigenvalues with exponential asymptotics generated by distant perturbations ⋮ On the Schrödinger equation with steplike potentials

Cites Work

• On the Riemann–Hilbert problem for the one-dimensional Schrödinger equation
• Low-energy behaviour of the scattering matrix for the Schrodinger equation on the line
• Inverse scattering. I. One dimension
• A factorization of the scattering matrix for the Schrödinger equation and for the wave equation in one dimension
• Inverse scattering on the line
• Wave scattering in one dimension with absorption
• Levinson’s theorem, zero-energy resonances, and time delay in one-dimensional scattering systems
• On the number of states bound by one-dimensional finite periodic potentials
• Factorization of scattering matrices due to partitioning of potentials in one-dimensional Schrödinger-type equations

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