Energy Spectrum of a Particle in an Infinitely Deep Potential Well with a Non-flat Bottom

Denysov, Stanislav Ivanovych; Husachenko, A.V.; Ryzhkov, O.S.

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Title	Energy Spectrum of a Particle in an Infinitely Deep Potential Well with a Non-flat Bottom
Authors	Denysov, Stanislav Ivanovych Husachenko, A.V. Ryzhkov, O.S.
ORCID	http://orcid.org/0000-0001-9590-1001
Keywords	наноструктури наноструктуры nanostructures квантова поведінка квантовое поведение quantum behavior
Type	Conference Papers
Date of Issue	2018
URI	http://essuir.sumdu.edu.ua/handle/123456789/67953
Publisher	Sumy State University
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Citation	Husachenko, A.V. Energy Spectrum of a Particle in an Infinitely Deep Potential Well with a Non-flat Bottom [Текст] / A.V. Husachenko, O.S. Ryzhkov, S.I. Denisov // Фізика, електроніка, електротехніка: матеріали та програма науково-технічної конференції, м. Суми, 5-9 лютого 2018 р. / Відп. за вип. С.І. Проценко. – Суми: СумДУ, 2018. – С. 28.
Abstract	To model the quantum behavior of current carriers in heterogeneous nanostructures, different potential wells and barriers are widely used. Of particular interest are those (including artificial ones) for which the corresponding Schrödinger equation can be solved exactly. One of them is an infinitely deep potential well with a flat bottom defined as 𝑈(𝑥) = ∞ for \|𝑥\| ≥ 𝑎 and 𝑈(𝑥) = 0 for \|𝑥\| < 𝑎. Here, we report on exact solution of the stationary Schrödinger equation in the case, when the potential bottom is non-flat, i.e., 𝑈(𝑥) = −𝑓𝑥 (𝑓 > 0) if \|𝑥\| < 𝑎. Physically, this means that the particle in the well is subjected to an external force 𝑓 in the 𝑥-direction.
Appears in Collections:	Наукові видання (ЕлІТ)