Upper and lower limits for the number of S-wave bound states in an attractive potential

DOI10.1063/1.1532107zbMath1062.81146arXivmath-ph/0210046OpenAlexW3099987058MaRDI QIDQ4832960

Francesco Calogero, Fabian Brau

Publication date: 14 December 2004

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

Full work available at URL: https://arxiv.org/abs/math-ph/0210046

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) (S)-matrix theory, etc. in quantum theory (81U20)

Related Items (10)

A new class of Pöschl–Teller potentials with inverse square singularity and their spectra using the asymptotic iteration method ⋮ Lower limit in semiclassical form for the number of bound states in a central potential ⋮ On the decrease of the number of bound states with the increase of the angular momentum ⋮ Upper limit on the number of bound states of the spinless Salpeter equation ⋮ Local approximation to the critical parameters of quantum wells ⋮ The auxiliary field method in quantum mechanics ⋮ Upper limit on the critical strength of central potentials in relativistic quantum mechanics ⋮ A class of (\(\ell\)-dependent) potentials with the same number of (\(\ell\)-wave) bound states ⋮ SEMIRELATIVISTIC HAMILTONIANS AND THE AUXILIARY FIELD METHOD ⋮ Upper bounds on the number of eigenvalues of stationary Schrödinger operators

Cites Work

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• Bounds on the number of eigenvalues of the Schrödinger operator
• The three-dimensional Fourier grid Hamiltonian method
• New bounds on the number of bound states for Schrödinger operators
• Upper and lower limits for the number of bound states in a given central potential
• The asymptotic eigenvalue distribution for non-smooth elliptic operators
• Bounds on the eigenvalues of the Laplace and Schroedinger operators
• On the number of bound states for the one-dimensional Schrödinger equation
• The Calogero bound for nonzero angular momentum
• Generalization of the Calogero–Cohn bound on the number of bound states
• On the Number of Bound States of a Given Interaction
• Sufficient Conditions for an Attractive Potential to Possess Bound States
• Strong Coupling Limit in Potential Theory. I
• On the Scattering of a Particle by a Static Potential
• On the Number of Bound States in a Central Field of Force

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