一维无限深势阱问题的可视化研究

Visualization Studies on One-dimensional Infinite Potential Well

采用解析法和可视化分析两种方法,对一维无限深势阱中微观粒子的能级、波函数和概率密度函数的特征进行了研究。结果表明:坐标轴的平移变换是求解一维无限深势阱中微观粒子的能级、波函数简洁可行的方法。随着势阱宽度增加,微观粒子体系能量减小,各能级之间的能量间隔减小;微观粒子的波函数和概率密度函数曲线与x轴有n+1个交点,波函数具有n个极值,概率密度函数具有2n-1个极值。

By using the analytic method and visualization method, the microparticle characteristic of energy, wave function and probability density function of micropavrtide in the one-dimensional infinite potential well are studied. The results show that the coordinate translation method is the simple possible way for solving the energy and wave function of microparticle in the one-dimensional infinite potential well. With the increasing of well width, the energies of the microparticle systems and the energy interval among energy levels become lower and lower.The wave function and probability density function curve of micro-particles intersect the x axis with n ＋1 point, the wave function with nextreme values, the probability density function with 2n-1 extreme values.