A Second Eigenvalue Bound for the Dirichlet Schrodinger Equation with a Radially Symmetric Potential
| dc.contributor.author | Haile, Craig | |
| dc.date.accessioned | 2019-12-18T18:30:58Z | |
| dc.date.available | 2019-12-18T18:30:58Z | |
| dc.date.issued | 2000-01-28 | |
| dc.description.abstract | We study the time-independent Schrodinger equation with radially symmetric potential k|x|α, k ≥ 0, k ∈ ℝ, α ≥ 2 on a bounded domain Ω in ℝn, (n ≥ 2) with Dirichlet boundary conditions. In particular, we compare the eigenvalue λ2 (Ω) of the operator -Δ + k|x|α on Ω with the eigenvalue λ2(S1) of the same operator -Δ + krα on a ball S<sub>1</sub>, where S<sub>1</sub> has radius such that the first eigenvalues are the same (λ1(Ω) = λ1(S1)). The main result is to show λ2(Ω) ≤ λ2(S1). We also give an extension of the main result to the case of a more general elliptic eigenvalue problem on a bounded domain Ω with Dirichlet boundary conditions. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 19 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Haile, C. (2000). A second eigenvalue bound for the Dirichlet Schrodinger equation wtih a radially symmetric potential. <i>Electronic Journal of Differential Equations, 2000</i>(10), pp. 1-19. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/9107 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2000, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Schrodinger eigenvalue equation | |
| dc.subject | Dirichlet boundary conditions | |
| dc.subject | Eigenvalue bounds | |
| dc.subject | Radially symmetric potential | |
| dc.title | A Second Eigenvalue Bound for the Dirichlet Schrodinger Equation with a Radially Symmetric Potential | |
| dc.type | Article |