基于延拓本征函数基构造的量子台球中的相干态
Coherent states in quantum billiards constructed in the basis of the continued eigenfunctions
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中文总结 AI 辅助
本文提出一种新方法，将高斯波函数向延拓的量子台球本征态基投影以构造量子台球的广义相干态，利用Balian--Bloch方程的预解式构建投影算子，对特定台球可通过两类θ函数解析表达相干态波函数。
中文摘要 AI 辅助
本文提出了一种构造量子台球中广义相干态的新方法，该相干态被定义为高斯波函数向延拓后的量子台球本征态基的投影，延拓过程作为定义在整个ℝ²上的等价Balian--Bloch方程的解来构建，投影算子则利用Balian--Bloch方程的预解式构造。对于一维势阱及属于Coxeter群的台球，相干态的波函数可通过雅可比θ函数和黎曼θ函数解析表达。
英文摘要
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.
