An analytical solution for conical quantum dots

In the paper, an analytical method of the solution of a governing nonlinear eigenproblem is proposed. It can be directly applied into analysis of axisymmetric conical quantum dots embedded in a matrix. The method is based on the use of variational formulation combined with the method of the Rayleigh quotient and the series expansions. In order to explain the form of the series expansions (the Bessel and sine series), the analytical solutions for quantum dots are demonstrated and discussed. The solved example shows the efficiency of the method.