Minimizing Schrödinger eigenvalues for confining potentials
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929429503016960 |
|---|---|
| author | Frank, Rupert L. |
| author_facet | Frank, Rupert L. |
| contents | We consider the problem of minimizing the lowest eigenvalue of the Schrödinger operator $-Δ+V$ in $L^2(\mathbb R^d)$ when the integral $\int e^{-tV}\,dx$ is given for some $t>0$. We show that the eigenvalue is minimal for the harmonic oscillator and derive a quantitative version of the corresponding inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15103 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimizing Schrödinger eigenvalues for confining potentials Frank, Rupert L. Analysis of PDEs Mathematical Physics Functional Analysis Spectral Theory We consider the problem of minimizing the lowest eigenvalue of the Schrödinger operator $-Δ+V$ in $L^2(\mathbb R^d)$ when the integral $\int e^{-tV}\,dx$ is given for some $t>0$. We show that the eigenvalue is minimal for the harmonic oscillator and derive a quantitative version of the corresponding inequality. |
| title | Minimizing Schrödinger eigenvalues for confining potentials |
| topic | Analysis of PDEs Mathematical Physics Functional Analysis Spectral Theory |
| url | https://arxiv.org/abs/2407.15103 |