Proper quantization rule approach to three-dimensional quantum dots


Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, Unidad Profesional Adolfo López Mateos, México D. F.07738, México. E-mail:


In this article, we develop a formalism to obtain the energy levels of the electron in a central force potential confined in a spherical quantum dot with radius rC by the proper quantization rule and the Wentzel-Kramers-Brillouin approximation. It is shown that the numerical results are in good agreement with exact solutions. To illustrate this method, we consider the linear harmonic oscillator and Coulomb potential confined within an impenetrable sphere of radius rC in three dimensions. © 2013 Wiley Periodicals, Inc.