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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.23466 |
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Table of Contents:
- In mathematical physics it is of interest to study Schrödinger equations with friction and possessing an invariant measure. The focus of this paper is the Cauchy problem for the Schrödinger equation $\p_t f - i \mathscr L f = 0$, where $\mathscr L = Δ- \sa x,\nabla\da$ is the Ornstein-Uhlenbeck operator. We use this as a model to stimulate interest in a new class of possibly degenerate dispersive equations which cannot be treated by the existing theory.