Analytical solution of the Schrödinger equation for an electron confined in a triangle-shaped quantum well

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• 作者：Gorley ; Peter N. ; Vorobiev ; Yuri V. ; Gonzá ; lez-Herná ; ndez ; Jesú ; s ; Horley ; Paul P.
• 关键词：Quantum well ; Energy ; Wave function ; Absorption spectrum
• 刊名：Microelectronic Engineering
• 出版年：2003
• 出版时间：April, 2003
• 年：2003
• 卷：66
• 期：1-4
• 页码：39-45
• 全文大小：143 K

文摘

For the triangular-shaped quantum well, the electron wave functions and energy values are found by analytical solution of the Shrödinger equation. In approximation of impenetrable walls, two sets of solutions are obtained, one corresponding to the symmetric, and the other to antisymmetric wave functions. The distributions of the probability density give a clear picture of standing waves in a triangular-shaped plate. The comparison of the system energy levels with those obtained for quasi-periodic boundary conditions give reasonable coincidence. The results obtained proved to be useful in explanation of electronic optical absorption spectra of some of the organic colorants, on the basis of FEMO approach (free electron molecular orbitals); it could be used for other nanosystems with particles of triangular shape.