广义边界条件和概率流密度的连续性

General boundary conditions and the continuity of probability current density

以四参量族———广义边界条件代替有限深方势阱内粒子波函数的对数的一阶导数连续性条件,表明这种替换比用广义边界条件取代一维盒子内自由粒子波函数在两壁处为零的边界条件显得更合理些.我们发现,如对参量ρ和θ取任意值,则会导致概率流密度连续性被破坏.我们找到了约束ρ和θ取值的条件,并得到一组新的解析解.

For a particle inside a one-dimensional finite-deep square well potential, we try to substitute the continuity condition of the first-order derivative of logarithm of wave functions by the general boundary conditions. It seems more reasonable than that replaceing the usual boundary condition forcing wave functions to vanish at two walls for a free particle confined in a one-dimensional box. It is found that the continuity condition of probability current density might be damaged, if the values of parameters ρ and θ are arbitrary. In addition, the constrained conditions for the parameters ρ and θ are given and a new class of analytical solutions is obtained.\;