论文标题
一种解决schrödinger方程的新方法
A new approach to solving the Schrödinger equation
论文作者
论文摘要
设计了一种新的方法，可以设计到一维量子机械系统的精确解决方案。该方案基于引入波函数的潜在函数及其满足的方程。我们恢复已知的解决方案，并获得新的溶液，以获得具有消失和非逐渐消失的BOHM电位的波形和相互作用的颗粒。对于大多数潜力，没有用于Schrödinger方程的解决方案产生消失的Bohm电位。一个（大但）受限制的潜力家族允许存在BOHM潜在消失的特定解决方案。确定了这个潜力家族，并提供了几个例子。结果表明，某些量子（例如加速的通风波形）是由于存在非变化的BOHM电位所致。找到并讨论了此类的新示例。
A new approach to find exact solutions to one--dimensional quantum mechanical systems is devised. The scheme is based on the introduction of a potential function for the wavefunction, and the equation it satisfies. We recover known solutions as well as to get new ones for both free and interacting particles with wavefunctions having vanishing and non--vanishing Bohm potentials. For most of the potentials, no solutions to the Schrödinger equation produce a vanishing Bohm potential. A (large but) restricted family of potentials allows the existence of particular solutions for which the Bohm potential vanishes. This family of potentials is determined, and several examples are presented. It is shown that some quantum, such as accelerated Airy wavefunctions, are due to the presence of non--vanishing Bohm potentials. New examples of this kind are found and discussed.
