Generalized comparison theorems in quantum mechanics
| dc.creator | Hall, Richard L. | |
| dc.creator | Katatbeh, Qutaibeh D. | |
| dc.date | 2002-08-30 | |
| dc.date.accessioned | 2026-07-07T04:29:23Z | |
| dc.date.available | 2026-07-07T04:29:23Z | |
| dc.description | This paper is concerned with the discrete spectra of Schroedinger operators H = -Delta + V, where V(r) is an attractive potential in N spatial dimensions. Two principal results are reported for the bottom of the spectrum of H in each angular-momentum subspace H_{ell}: (i) an optimized lower bound when the potential is a sum of terms V(r) = V^{(1)}(r) + V^{(2)}(r), and the bottoms of the spectra of -Delta + V^{(1)}(r) and -Delta + V^{(2)}(r) in H_{ell} are known, and (ii) a generalized comparison theorem which predicts spectral ordering when the graphs of the comparison potentials V^{(1)}(r) and V^{(2)}(r) intersect in a controlled way. Pure power-law potentials are studied and an application of the results to the Coulomb-plus-linear potential V(r) = -a/r + br is presented in detail: for this problem an earlier formula for energy bounds is sharpened and generalized to N dimensions. | |
| dc.description | 25 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/math-ph/0208047 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0208047 | |
| dc.identifier | J. Phys. A 35, 8727-8742 (2002) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/57137 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Quantum Physics | |
| dc.title | Generalized comparison theorems in quantum mechanics | |
| dc.type | text |