论文标题
Feynman Checkers：数字理论属性
Feynman checkers: number-theoretic properties
论文作者
论文摘要
我们研究Feynman Checkers，这是R. Feynman引入的电子运动的基本模型。在此型号中，一个棋盘在棋盘上移动，我们计算转弯。 Feynman Checkers也被称为一维量子步行。我们证明了该模型中一些新的数字理论结果，例如，在特定区域中电子波函数的真实部分和虚构部分的符号交替。我们所有的结果都可以用年轻的图表来说明，即，我们比较了奇数和偶数步骤的年轻图的数量。
We study Feynman checkers, an elementary model of electron motion introduced by R. Feynman. In this model, a checker moves on a checkerboard, and we count the turns. Feynman checkers are also known as a one-dimensional quantum walk. We prove some new number-theoretic results in this model, for example, sign alternation of the real and imaginary parts of the electron wave function in a specific area. All our results can be stated in terms of Young diagrams, namely, we compare the number of Young diagrams with an odd and an even number of steps.
