The Schrodinger equation of two-dimensional and three-dimensional infinite deep annular potential wells is solved by the method of separating variables. The eigenvalue of the radial wave function is determined by the zero point of the cross product combination of the Bessel function. For the three-dimensional case, the analyticalsolution of the ground state wave function can be obtained. For the excited state wave function, the radial probability density distribution is given by numerical method. For the two-dimensional infinite deep annular potential well, the radial probability density distributions of ground state and excited state are given by numerical method.