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Kuban State Technological University, Moskovskaya 2 str., Krasnodar 350072, Russia
Received: November 30, 2011 / Accepted: December 28, 2011 / Published: February 25, 2012.
Abstract: Studying of properties of quantum rings (nano-size and mesoscoping) in a magnetic field is one of directions on which there are interesting results. Quantum transitions in such structures are accompanied by radiation on border of infra-red light, and interest is caused by periodic structures in quantum rings or six-angular cells are cooperate with problems of pseudo-crystal construction. In this work results of calculations are shown of such structure in two-dimension statement (periodicity is provided with decomposition of the solution and confining potential in Fourier series on both spatial coordinates) are presented.
Mathematical modeling of quantum effects on the basis of Schr?dinger equation (with action of a magnetic field) give an example of the various materials on structure that can show almost identical quantum properties. For an example of such numerical solution two-dimensional periodic structures (lattices), and are chosen, the requirement of spatial periodicity is a necessary condition for coinciding of their quantum properties in strict mathematical sense. One of lattices has type of so-called quantum rings, and such nano-size structures now are investigated experimentally [1].
2. Method of Computation
The solution of stationary equation Schr?dinger in two-dimensional linear statement is considered.
Received: November 30, 2011 / Accepted: December 28, 2011 / Published: February 25, 2012.
Abstract: Studying of properties of quantum rings (nano-size and mesoscoping) in a magnetic field is one of directions on which there are interesting results. Quantum transitions in such structures are accompanied by radiation on border of infra-red light, and interest is caused by periodic structures in quantum rings or six-angular cells are cooperate with problems of pseudo-crystal construction. In this work results of calculations are shown of such structure in two-dimension statement (periodicity is provided with decomposition of the solution and confining potential in Fourier series on both spatial coordinates) are presented.
Mathematical modeling of quantum effects on the basis of Schr?dinger equation (with action of a magnetic field) give an example of the various materials on structure that can show almost identical quantum properties. For an example of such numerical solution two-dimensional periodic structures (lattices), and are chosen, the requirement of spatial periodicity is a necessary condition for coinciding of their quantum properties in strict mathematical sense. One of lattices has type of so-called quantum rings, and such nano-size structures now are investigated experimentally [1].
2. Method of Computation
The solution of stationary equation Schr?dinger in two-dimensional linear statement is considered.