Coherent states in quantum billiards constructed in the basis of the continued eigenfunctions

• URL: http://arxiv.org/abs/2608.20302v1
• Date: Thu, 20 Aug 2026 17:40:18 GMT
• Title: Coherent states in quantum billiards constructed in the basis of the continued eigenfunctions
• Abstract summary: The coherent states are defined as the projections of a Gaussian wave function on the basis of the eigenstates of the quantum billiard, continued outside.<n>In the case of the one-dimensional potential well and billiards, belonging to the Coxeter group, the wave functions of the coherent states were expressed analytically via the Jacobi and theta functions.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the article a new approach to construction of generalized coherent states in quantum billiards is proposed. The coherent states are defined as the projections of a Gaussian wave function on the basis of the eigenstates of the quantum billiard, continued outside. The continuation is built as the solution of the equivalent Balian--Bloch equation, defined on the entire $\mathbb{R}^2$ and the projection operator is built using the resolvent of the Balian--Bloch equation. In the case of the one--dimensional potential well and billiards, belonging to the Coxeter group, the wave functions of the coherent states were expressed analytically via the Jacobi and Riemann theta functions.

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