Strong maximum and anti-maximum principles are extended to weak L 2 (R 2 )solutions u of the Schro dinger equation &2u+q(x) u&\*u= f (x) in L 2 (R 2 ) in the following form: Let . 1 denote the positive eigenfunction associated with the principal eigenvalue \* 1 of the Schro dinger operator A=&2+q(x)
Maximum entropy approach to Schrödinger's radial equation
✍ Scribed by F. Garcias; M. Casas; A. Plastino
- Publisher
- John Wiley and Sons
- Year
- 1995
- Tongue
- English
- Weight
- 596 KB
- Volume
- 507
- Category
- Article
- ISSN
- 0003-3804
No coin nor oath required. For personal study only.
✦ Synopsis
From the sole knowledge (at a finite number of points) of the numerical values of the potential V ( r ) corresponding to Schrodinger's radial equation, it is found that recourse to Information Theory (IT) concepts allows one to infer the pertinent wave functions (and eigenvalues) without attempting to solve the concomitant differential equation. Moreover, the underlying IT ideas allow for an analytical treatment that yields exact wave functions of the maximum (quantal) entropy form in a number of cases of interest.
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