Abstract 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 Schrodinger 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.

中文翻译：

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求解薛定谔方程的新方法

摘要 设计了一种寻找一维量子力学系统精确解的新方法。该方案基于引入波函数的势函数及其满足的方程。我们恢复已知的解决方案，并为具有消失和非消失玻姆势的波函数的自由和相互作用粒子获得新的解决方案。对于大多数势，薛定谔方程的解都不会产生消失的玻姆势。一个（大但）受限的势族允许存在玻姆势为零的特定解。确定了这个电位族，并给出了几个例子。结果表明，一些量子，例如加速的艾里波函数，是由于非零玻姆势的存在。