1. Ground state energy bounds for potentials ‖x‖ν
- Author
-
Mary Hall Reno and R. E. Crandall
- Subjects
Numerical analysis ,Mathematical analysis ,Recursion (computer science) ,Statistical and Nonlinear Physics ,Schrödinger equation ,symbols.namesake ,Bounded function ,Arbitrary-precision arithmetic ,symbols ,Ground state ,Computer Science::Databases ,Mathematical Physics ,Eigenvalues and eigenvectors ,Schrödinger's cat ,Mathematics - Abstract
A theory is developed from which both upper and lower analytic bounds on Schrodinger 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.
- Published
- 1982
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