论文标题
相位空间schrödinger方程的渐近学
Asymptotics for the Phase Space Schrödinger Equation
论文作者
论文摘要
我们考虑相位空间方程的半古典时间演变。我们通过各向异性高斯近似构建半古典相位空间传播器，与附近的轨道近似有关。我们在双相空间中推断出典型的系统，该系统与Berezin-Shubin-Marinov的规范系统有关，并为初始WKB状态的相位空间schrödinger方程构建了Cauchy问题的半经典渐近解决方案。我们说明了$ \ mathbb {r} $中次级电位的方法。
We consider semi-classical time evolution for the phase space Schrödinger equation. We construct a semi-classical phase space propagator in terms of semi-classical wave packets by the Anisotropic Gaussian Approximation, related to the Nearby Orbit Approximation. We deduce the canonical system in double phase space, related to the Berezin-Shubin-Marinov canonical system and construct a semi-classical asymptotic solution of the Cauchy problem for the phase space Schrödinger equation for initial WKB states. We illustrate the method for sub-quadratic potentials in $\mathbb{R}$.
