Eigenvalue Problems for Two-Dimensional Continuous Schrödinger Equation with Non-parabolic Effective Mass Approximation

• Main Authors: Meng-Jie Lin, 林盟傑
• Other Authors: Wen-Wei Lin
• Format: Others
• Language: en_US
• Online Access: http://ndltd.ncl.edu.tw/handle/69501212282640840394

碩士 === 國立清華大學 === 數學系 === 92 === This paper is devoted to investigate the two-dimensional continuous Schr dinger equation with non-parabolic effective mass approximation. Our results primarily concern the number of energy states lying in the confinement potential well. The article is organized as follows. First, we introduce the derivation of the model problem, the Bessel’s equation and the modified Bessel’s equation. At the same time, we also list some useful properties of the Bessel functions and the modified Bessel functions. Next, we construct a characteristic equation whose roots are eigenvalues of the model problem. It is a key equation. We have to use it to finish some main results. Finally, we discuss some properties of the characteristic equation, roughly sketch the graph of the characteristic equation and state the main results that we have finished.