Qiuru Wang

Ulink High School of Suzhou Industrial Park

Abstract：

This paper introduces an important branch of quantum mechanics—quantum tunneling. The main objective is to compute and analyze quantum tunneling probabilities at different scales (macroscopic and microscopic). We first outline the derivation of the tunneling formula, detailing the conditions and principles necessary for tunneling to occur. Then, using the tunneling equation, we calculate the tunneling probabilities of electrons and protons under specific potential barriers and describe a practical application of quantum tunneling—scanning tunneling microscopy (STM). Finally, we attempt to estimate and discuss the probability and feasibility of a macroscopic object (i.e., a human) undergoing quantum tunneling. Our calculations show the tunneling probability for a human passing through a wall is astronomically small (effectively zero), demonstrating that macroscopic tunneling is physically impossible.

Key Words：

quantum tunneling; potential barrier; tunneling formula; tunneling probability