Abstract: A new type of potential well, namely one dimensional infinitely trapezoid potential well, which is simple in form but rich in content, is studied by us with the help of special functions and the semi-analytical solutions of the wave functions and energy levels for a micro-particle confined into it is obtained. Those results can help us better understand the physical mechanism of the two-dimensional electron gas in trapezoid channel potential well. Besides, the connection and difference between the model proposed in this paper and the well-known models, i.e. rectangular/triangular potential well are illustrated. We also discuss the properties of the wave function based on the correspondence principle.

Key words: trapezoid potential well, wave function, energy level, correspondence principle