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Smoothed wave functions of chaotic quantum systems
Affiliation:1. School of Physics, Northwest University, Xi’an, Shaanxi 710069, China;2. National Key Laboratory of Photoelectric Technology and Functional Materials (Culture Base), and Institute of Photonics and Photon-Technology, Northwest University, Xi’an, Shaanxi 710069, China;1. School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044, China;2. College of Science, Minzu University of China, Beijing 100081, China;1. Instituto de Física, Universidade Federal de Alagoas, 57072-970, Maceió-AL, Brazil;2. Departamento de Física, Universidade Federal do Paraná, 81531-990, Curitiba-PR, Brazil
Abstract:It is shown that wave functions of quantum systems as ħ → 0 have an extra density near unstable periodic trajectories of the classical problem. The averaged wave function square is represented as the sum over a finite number of periodic trajectories. The contribution of each trajectory is expressed through the elements of the monodromy matrix of the trajectory. The results are compared with the numerical calculations of the wave functions for the stadium billiard.
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