A quantum mechanical problem concerning the penetration of two particles in the bound state (the complex particle) through the potential barrier is treated. Accounting for the internal structure of the complex particle leads to an effective spreading of the potential barrier that facilitates the penetration through the barrier. (auth)
At the turn of the twentieth century, the establishment of quantum theory propelled rapid advancements, particularly in the understanding of quantum tunnelling—a fundamental phenomenon in quantum mechanics crucial for various physical processes. The quantum phenomenon of particle passes through potential barriers is of great importance. In classical physics, when the energy of a particle is less than the height of a double barrier structure, it is impossible for it to pass through. However, quantum mechanics allows a particle to penetrate the barrier and emerge on the other side. This paper explores the quantum tunnelling effect, focusing on the single potential barrier model in one dimension and subsequently extending to the double potential barrier model. The Schrödinger equation provides the foundational framework for elucidating the motion of microscopic particles, emphasizing wave-particle duality inherent in quantum mechanics. The analysis of the single potential barrier model involves solving the Schrödinger equation in different regions, determining wave functions and coefficients through boundary conditions. The transmission coefficient is derived, representing the probability of a particle passing through a barrier. In the case of a “thick” barrier, an approximate form for transmission coefficient is provided, demonstrating the exponential decrease in transmission probability with increasing barrier thickness.
In this paper,transmission coefficient that the micro particle penetrate two potential barriers successively is calculated by solving the stationary schrodinger equation.Our numerical results show that the micro particle could penetrate potential barriers no matter energy of particle is taller or smaller than the height of potential barriers.But the transmission coefficient varies in several different circumstances.Particularly,it may arise resonance transmission in conditions.In a word,the transmission coefficient could changes with the height and width of two potential barriers,and have nothing to do with the distance between two potential barriers.