Ground state energy bounds for potentials ‖x‖ν
- 1 January 1982
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 23 (1) , 64-70
- https://doi.org/10.1063/1.525207
Abstract
A theory is developed from which both upper and lower analytic bounds on Schrödinger eigenvalues can be obtained. We propose a recursion algorithm with which ground energies for certain potentials can be rigorously bounded to arbitrary precision. These analytic and numerical methods, together with existing techniques, are applied to the ground state problem for power potentials ‖x‖ν, ν≳0.Keywords
This publication has 12 references indexed in Scilit:
- Quarkonium spectroscopy in a potential model with vacuum-polarization correctionsPhysical Review D, 1980
- Approximations to the eigenvalues of the Hamiltonian P2+A mod Xnumod in the Weyl correspondence limit-a critical appraisal of Turschner's formulaJournal of Physics A: General Physics, 1979
- Exact eigenvalues of the Hamiltonian P2+A mod X modnuJournal of Physics A: General Physics, 1979
- Vacuum-polarization-corrected long-distance static quark-antiquark potentialPhysical Review D, 1979
- Lower bounds for quantum mechanical energy levelsJournal of Physics A: General Physics, 1978
- Lower Bounds for EigenvaluesPhysical Review B, 1947
- On the Connection Formulas and the Solutions of the Wave EquationPhysical Review B, 1937
- Neue Berechnung der Energie des Heliums im Grundzustande, sowie des tiefsten Terms von Ortho-HeliumThe European Physical Journal A, 1929
- The behavior of a boundary value problem as the interval becomes infiniteTransactions of the American Mathematical Society, 1928
- Eine Verallgemeinerung der Quantenbedingungen f r die Zwecke der WellenmechanikThe European Physical Journal A, 1926