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Complex energy of the quasistationary states in ideal quantum dots in external electric field

Keywords:

A.M. Mandel – Ph.D.(Phys.-Math.), Associate Professor, Department of Physics, Moscow State University of Technology «STANKIN»
E-mail: arkadimandel@mail.ru
V.B. Oshurko – Dr.Sc.(Phys.-Math.), Head of Department of Physics, Moscow State University of Technology «STANKIN»
E-mail: vbo08@yandex.ru
K.G. Solomakho – Post-graduate Student, Department of Physics, Moscow State University of Technology «STANKIN»
E-mail: kirgeosol@gmail.ru


Ideal quantum dots are so small that they are capable of only one localized electron. Simple spectrum makes them attractive for nu-merous applications. Quasi-stationary States of electrons in such quantum dots is considered. They are quasi-stationary because of the possibility of tunneling transition of an electron in a continuous spectrum due to the electric field. The energy of such States is complex, and the wave function (it is called Gamow) describes a formally divergent integral. This creates a significant mathematical problem. This paper proposes a new method of regularization of Gamow wave function in the electric field. The basic idea of our method is the introduction of the field strength infinitesimal imaginary Supplement. The binding energy and the probability of ejection of the electron by the electric field from the pit of finite size is calculated in this way. It shows that there are oscillations of the stark shift and level width in a constant electric field. This is the main difference between the results obtained from previously known, obtained in the approximation of the Delta potential. They very significantly affect the spectrum of an ideal quantum dots. This method of regularization of the Gamow wave function is applicable to any system if their collapse causes an electric field.

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