Abstract: The energy levels and the wave functions of a particle in an infinitely deep potential well are investigated by virtue of the linear variational method and solving the generalized eigenvalue equation. The trial basis functions are composed of the independent polynomials which satisfy the continuous condition. It is indicated that the results of the linear variational method converge to the exact analytical results with the increase of the number of the＂ trial basis functions.

Key words: infinitely deep potential well, linear variational method, energy levels, wave functions, generalized eigenvalue equation