基于一种非分离变量方法，讨论了三种二维三角形量子结构中的电子态，包括半等边三角形、等腰直角三角形与等边三角形，得到了精确解析的电子波函数与能级方程.以AlN半导体材料参数进行了数值计算，并讨论了这些三角形量子结构的能级结构与波函数分布特点.

Using a nonseparable variable approach, the electronic energy spectra and wave-functions of 2D triangular quantum structures, including the hemi-equilateral triangle, the isosceles triangle, and the equilateral triangle are deduced and analyzed. The exact and analytical electronic states and energy-level equations in the three types of triangular structures are obtained. Numerical calculations are performed based on the material parameter of typical AlN semiconductor. The energy-level structures and wave-function distributions of electronic states are discussed in detail. The result reveals that the symmetry of the triangular quantum structure plays an important role in the energy-level structures and wave-function distributions of the triangular quantum structures