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Journal of Physics Conference Series

Quantum tunneling of molecules through compound barriers

Valentina A. Poteryaeva, Mikhail Alekseevich Bubenchikov, Soninbayar Jambaa, D Gankhuyag, D Tsedenbaya

Published May 1, 2020• 2 citations
Publisher

Abstract

Abstract The use of hydrogen and helium as a fuel requires well-developed technologies for the separation of gas mixtures, in particular, separation of isotopes of an element. The presence of quantum effects makes such processes possible, and the proposed system of two potential barriers enhances the differences in the passage of isotopes through two layers of matter providing high separation efficiency. The probability of atoms passing through composite barriers is derived from the solving of stationary Schrodinger equation.

DOI
10.1088/1742-6596/1537/1/012008

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Abstract The use of hydrogen and helium as a fuel requires well-developed technologies for the separation of gas mixtures, in particular, separation of isotopes of an element. The presence of quantum effects makes such processes possible, and the proposed system of two potential barriers enhances the differences in the passage of isotopes through two layers of matter providing high separation efficiency. The probability of atoms passing through composite barriers is derived from the solving of stationary Schrodinger equation.
An analytical solution to the problem of wave transport of matter through composite hyper-fine barriers is constructed. It is shown that, for a composite membrane consisting of two identical ultra-thin layers, there are always distances between the layers at which the resonant passage of one of the components is realized. Resonance makes it possible to separate de Broiler waves of particles with the same properties, which differ only in masses. Broad bands of hyper-selective separation of a hydrogen isotope mixture are found at the temperature of 40 K.
This paper focuses on the quantum tunneling effect, which describes how a particle may penetrate barriers or obstructions using the Schrödinger equation. If a particle makes a barrier tunneling, it means that a particle with low energy goes through the barrier whose energy level is much higher. It is a basis or background for the entire theory of this part. The particle transport probability is explained using both single- and multi-barrier system models. The paper studies the relationship between barrier parameters and particle transmission probability for both single- and multiple-barrier system models.The aim of the study is the provision of the theoretical devices and algorithms via a quantum operational efficiency.Particularly, the paper deals with the multipath barrier tunneling effect, and it connects the transmission coefficients with the system parameters. The goal of this article is to come up with the new strategies and procedures that one can use the quantum phenomenon of the tunneling effect in the contemporary physical th applications, cutting the gap between theoretical physics and technology.This will be done by studying and analyzing theoretical processes and mathematics of this phenomenon along with the technological applications it has.
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.
This research paper explores the theoretical foundations of quantum tunneling, explaining how particles can pass through potential barriers despite lacking the classical energy to do so. It develops the mathematical framework using the Schrödinger equation, derives the transmission coefficient for a rectangular potential barrier, introduces the WKB approximation for more realistic barriers, and examines key applications such as alpha decay, scanning tunneling microscopy (STM), and the Josephson effect. The paper also reviews the historical development, experimental verification, and limitations of quantum tunneling, highlighting its significance as one of the most fundamental and experimentally validated predictions of quantum mechanics.