An Analytical Solution to the Problem of Hydrogen Isotope Passage through Composite Membranes Made from 2D Materials

Alexey Mikhailovich Bubenchikov,Anna Sergeevna Chelnokova,Soninbayar Jambaa,Mikhail Alekseevich Bubenchikov

doi:10.3390/math9192353

Abstract

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.

Highlights

It becomes necessary to solve the Schrödinger equation, which is one of the most important equations of mathematical physics in modeling the processes of low-temperature separation of gas components
A fairly large number of modern works are devoted to solving the nonlinear Schrödinger equation (NLSE)
In its form, the Schrödinger integral equation is analogous to an integral equation with a degenerate kernel

Summary

Introduction

It becomes necessary to solve the Schrödinger equation, which is one of the most important equations of mathematical physics in modeling the processes of low-temperature separation of gas components. A fairly large number of modern works are devoted to solving the nonlinear Schrödinger equation (NLSE). A method for constructing a class of exact analytical solutions of the NLSE model with varying dispersion, nonlinearity, as well as gain or absorption, is developed in [1]. Using the Lie symmetry method, new solutions for nonlinear Schrödinger systems are constructed in [2]. A number of works are devoted to the study of solitons [8] and their stability [9], as well as to the question of soliton perturbations [10]. In [11], the authors suggest an exact analytical resolution method for stationary Schrödinger equations with polynomial potentials

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Conclusion