Spectral Analysis of the Quantization of a Mixed System
نویسنده
چکیده
We investigate the quantization of a free particle interacting linearly with a harmonic oscillator. We extend the work of previous authors to obtain accurate and reliable estimates for the large energy levels in order to determine the spectral statistics of the system. We do this via an analytical study of the system in the two complementary regions of phase space, followed by attempts to undertake the requisite matching of the solutions numerically. We use matching conditions to obtain good approximations to a large number of eigenvalues, from which the statistics can be determined and compared with the long-standing conjectures as to their nature. This task has been started, but more work needs to be undertaken to complete the study.
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