论文标题
通过经典苛刻的边界值来构建不可分离但可整合的二维哈密顿系统的量子波函数
Construction of quantum wavefunctions for non-separable but integrable two-dimensional Hamiltonian systems by means of the boundary values on the classical caustics
论文作者
论文摘要
结果表明，可以通过解决特定的经典轨迹家族在与量子状态的一对一相关的区域内部和外部构建量子波函数，以解决特定经典轨迹家族跨越的区域内外的合适的dirichlet边界值问题，以构建量子波函数。该方法既适用于Schrodinger方程，又应用于量子Hamilton-Jacobi方程。边界值是通过在包围经典轨迹的苛性弧上集成一二级方程来获得的。这种方法给出了与通常的方法相同的结果，并阐明了量子和经典力学之间的联系。
It is shown that it is possible to construct the quantum wave functions for non-separable but integrable two-dimensional Hamiltonian systems, by solving suitable Dirichlet boundary values problems inside and outside the regions spanned by particular families of classical trajectories, in one-to-one correspondence with the quantum state. The method is applied both to the Schrodinger equation, and to the quantum Hamilton-Jacobi equation. The boundary values are obtained by integrating the one-dim equations on the caustics arcs enveloping the classical trajectories. This approach gives the same results as the usual methods, and furthermore clarifies the links between quantum and classical mechanics.
