Energy transport in the Schrödinger plate
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909977077088256 |
|---|---|
| author | Gavrilov, Serge N. Krivtsov, Anton M. Shishkina, Ekaterina V. |
| author_facet | Gavrilov, Serge N. Krivtsov, Anton M. Shishkina, Ekaterina V. |
| contents | In this paper, we introduce "the Schrödinger plate." This is an infinite two-dimensional linear micro-polar elastic medium, with out-of-plane degrees of freedom, lying on a linear elastic foundation of a special kind. Any free motion of the plate can be corresponded to a solution of the two-dimensional Schrödinger equation for a single particle in the external potential field $V$. The specific dependence of the potential $V$ on the position is taken into account in the properties of the plate elastic foundation. The governing equations of the plate are derived as equations of the two-dimensional constraint Cosserat continuum using the direct approach. The plate dynamics can be described by the classical Germain-Lagrange equation for a plate, but the strain energy is different from the one used in the classical Kirchhoff-Love plate theory. Namely, the Schrödinger plate cannot be imagined as a thin elastic body composed of an isotropic linear material. The main property of the Schrödinger plate is as follows: the mechanical energy propagates in the plate exactly in the same way as the probability density propagates according to the corresponding Schrödinger equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22898 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Energy transport in the Schrödinger plate Gavrilov, Serge N. Krivtsov, Anton M. Shishkina, Ekaterina V. Classical Physics Quantum Physics In this paper, we introduce "the Schrödinger plate." This is an infinite two-dimensional linear micro-polar elastic medium, with out-of-plane degrees of freedom, lying on a linear elastic foundation of a special kind. Any free motion of the plate can be corresponded to a solution of the two-dimensional Schrödinger equation for a single particle in the external potential field $V$. The specific dependence of the potential $V$ on the position is taken into account in the properties of the plate elastic foundation. The governing equations of the plate are derived as equations of the two-dimensional constraint Cosserat continuum using the direct approach. The plate dynamics can be described by the classical Germain-Lagrange equation for a plate, but the strain energy is different from the one used in the classical Kirchhoff-Love plate theory. Namely, the Schrödinger plate cannot be imagined as a thin elastic body composed of an isotropic linear material. The main property of the Schrödinger plate is as follows: the mechanical energy propagates in the plate exactly in the same way as the probability density propagates according to the corresponding Schrödinger equation. |
| title | Energy transport in the Schrödinger plate |
| topic | Classical Physics Quantum Physics |
| url | https://arxiv.org/abs/2512.22898 |