Diffusion Process Representations for a Scalar-Field Schrödinger Equation Solution in Rotating Coordinates
Diffusion Process Representations for a Scalar-Field Schrödinger Equation Solution in Rotating Coordinates
复制标题
旋转坐标中标量场薛定谔方程解的扩散过程表示
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Ruobing Zhao
中科院分区：
文献类型：
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作者：
W. McEneaney;Ruobing Zhao
一类特殊的薛定谔初值问题被认为是，其中一个粒子在一个标量场运动的原点为中心，更具体地说，与薛定谔方程的解决方案的分布具有可忽略不计的质量在附近的原点。薛定谔方程被转换为去量子化的形式，并采用沿着经典粒子的轨迹为中心的非惯性系。通过使用复值扩散过程表示，在光滑性假设下，扩展收敛到真正的解决方案，在一个小参数的一系列扩展的解决方案近似。在只通过空间变量中的立方项展开的情况下，存在近似解，这些近似解与经典粒子的周期是周期性的，但具有额外的长期扰动。直到有限阶的解所需的计算是纯解析的。
A particular class of Schrodinger initial value problems is considered, wherein a particle moves in a scalar field centered at the origin, and more specifically, the distribution associated to the solution of the Schrodinger equation has negligible mass in the neighborhood of the origin. The Schrodinger equation is converted to the dequantized form, and a non-inertial frame centered along the trajectory of a classical particle is employed. A solution approximation as a series expansion in a small parameter is obtained through the use of complex-valued diffusion-process representations, where under a smoothness assumption, the expansion converges to the true solution. In the case of an expansion up through only the cubic terms in the space variable, there exist approximate solutions that are periodic with the period of a classical particle, but with an additional secular perturbation. The computations required for solution up to a finite order are purely analytical.