论文标题
经典粒子的量子行为受到随机力
Quantum behavior of a classical particle subject to a random force
论文作者
论文摘要
我们对schrodinger方程是否可以源自粒子的牛顿力学中的潜在力量中的牛顿力学来给出部分答案。我们表明，根据振荡器的频率和能量，施罗宾格方程在一段时间内可以描述一维谐波振荡器的经典运动的波动。我们通过得出尼尔森随机制定的量子制剂的假设，取决于量子力学的随机力，具体取决于小参数。我们表明，只要总电位保留运动的周期性，频率较小，则相同的结果适用于谐波振荡器周围的小潜在扰动。我们还表明，可以选择噪声光谱以获得固定质量的所有振荡器频率的结果。我们讨论了启发式方法，以概括一个粒子在一个维度中的结果，在可以使用动作角变量描述运动的电位中。
We give a partial answer to the question whether the Schrodinger equation can be derived from the Newtonian mechanics of a particle in a potential subject to a random force. We show that the fluctuations around the classical motion of a one dimensional harmonic oscillator subject to a random force can be described by the Schrodinger equation for a period of time depending on the frequency and the energy of the oscillator. We achieve this by deriving the postulates of Nelson's stochastic formulation of quantum mechanics for a random force depending on a small parameter. We show that the same result applies to small potential perturbations around the harmonic oscillator as long as the total potential preserves the periodicity of motion with a small shift in frequency. We also show that the noise spectrum can be chosen to obtain the result for all oscillator frequencies for fixed mass. We discuss heuristics to generalize the result for a particle in one dimension in a potential where the motion can be described using action-angle variables.
