论文标题
在最小长度的情况下，无限的方孔电势是有限方孔电势的限制情况
An infinite square-well potential as a limiting case of a finite square-well potential in a minimal-length scenario
论文作者
论文摘要
量子力学中研究的最广泛问题之一是无限的方孔电势。在最小长度的情况下，其研究需要额外的护理，因为井壁的边界条件不能很好地固定。为了避免这种情况，我们解决了有限的方孔电势，即使在最小长度的情况下，边界条件也是固定的，然后我们采取了到无穷大的势限，以找到无限平方孔电位的特征函数和能量方程。尽管对能量特征值的首次校正与文献相同，但我们的结果表明，特征功能在方形孔壁上具有第一个衍生物连续的连续，这是先前作品的分歧。那是因为在文献中，作者忽略了双曲线溶液，并假定了在无限方螺旋壁的壁上的第一个衍生物的不连续性，这是不正确的。如我们所示，在方形壁壁上的第一个特征函数的第一个衍生物的连续性确保了概率电流密度的连续性和时间演化的单位性
One of the most widely problem studied in quantum mechanics is of an infinite square-well potential. In a minimal-length scenario its study requires additional care because the boundary conditions at the walls of the well are not well fixed. In order to avoid this we solve the finite square-well potential whose the boundary conditions are well fixed, even in a minimal-length scenario, and then we take the limit of the potential going to infinity to find the eigenfunctions and the energy equation for the infinite square-well potential. Although the first correction for the energy eigenvalues is the same one has been found in the literature, our result shows that the eigenfunctions have the first derivative continuous at the square-well walls what is in disagreement those previous work. That is because in the literature the authors have neglected the hyperbolic solutions and have assumed the discontinuity of the first derivative of the eigenfunctions at the walls of the infinite square-well which is not correct. As we show, the continuity of the first derivative of the eigenfunctions at the square-well walls guarantees the continuity of the probability current density and the unitarity of the time evolution
