Abstract: In the finite difference calculations of the time-independent Schrödinger

equation， the mostly used difference formula is the central difference formula， which is

accompanied with a truncation error on the second-or- der of step-size. In this paper， the

fourth-order accurate difference formulas of the derivatives are derived by the

five-point polynomial interpolation， and used to solve time - independent Schrödinger

equation in several common potential wells. The numerical results show that， the

fourth - order accurate difference formula has better

convergence and higher precision than the common central difference formula.

Key words: high precision, difference method, interpolation, potential well, ground-state energy