Simple Examples of Position-Momentum Correlated Gaussian Free-Particle Wave Packets in One Dimension With the General Form of the Time-Dependent Spread in Position
Simple Examples of Position-Momentum Correlated Gaussian Free-Particle Wave Packets in One Dimension With the General Form of the Time-Dependent Spread in Position
复制标题
一维位置动量相关高斯自由粒子波包的简单例子，具有位置时相关扩展的一般形式
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发表时间：
2005
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通讯作者：
L. Bassett
中科院分区：
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作者：
R. Robinett;M. Doncheski;L. Bassett
我们提供一维自由粒子薛定谔方程的封闭式高斯波包解的简单示例，它表现出位置随时间扩展的最一般形式，即 (Δxt)2 = (Δx0)2 + At + (Δp0)2t2/m2，其中 A ≡ ´(?? − ´??›0)(?? − ´??›0) + (?? − ´??›0)(?? − <??>>0)>>0包含初始波包的位置-动量相关结构的信息。我们展示了与压缩状态相对应的简单示例，以及准经典情况，其中 A < 0，因此由于这种相关性，头寸价差可以（至少在最初）随时间减小。我们讨论如何在各种束缚态系统中动态生成（至少在概念上）这些示例中的初始相关性。最后，我们专注于提供不同的方法来可视化这些情况下存在的 x − p 相关性，包括动能的时间相关分布和维格纳准概率分布的使用。对于粒子受到均匀力的情况，我们讨论了与时间相关的 Δxt 和特殊相关解的类似结果。
We provide simple examples of closed-form Gaussian wave packet solutions of the free-particle Schrödinger equation in one dimension which exhibit the most general form of the time-dependent spread in position, namely (Δxt)2 = (Δx0)2 + At + (Δp0)2t2/m2, where A ≡ ‹(?? − ‹??›0)(?? − ‹??›0) + (?? − ‹??›0)(?? − ‹??›0)›0 contains information on the position-momentum correlation structure of the initial wave packet. We exhibit straightforward examples corresponding to squeezed states, as well as quasi-classical cases, for which A < 0 so that the position spread can (at least initially) decrease in time because of such correlations. We discuss how the initial correlations in these examples can be dynamically generated (at least conceptually) in various bound state systems. Finally, we focus on providing different ways of visualizing the x − p correlations present in these cases, including the time-dependent distribution of kinetic energy and the use of the Wigner quasi-probability distribution. We discuss similar results, both for the time-dependent Δxt and special correlated solutions, for the case of a particle subject to a uniform force.