Abstract: We introduce an algorithm, namely the celebrated Numerov algorithm, which is used to solve boundary value problem of two-order ordinary differential equation, and we obtain the numerical solution of the wave functions and energy levels of the particle confined into the one dimensional infinitely trapezoid potential well along with the shooting method. Besides, we get the ground state energy of the model through variational method.

Key words: Schrodinger＇ s equation, trapezoid potential well, Numerov algorithm, variational method