Abstract: For a nonlinear harmonic oscillator with potential V（x）=1/2mω2x2＋λx4,the classical equation of motion can not be solved by the perturbation method.The classical solution of the nonlinear oscillator is derived from quantum matrix elements by using the Heisenberg correspondence principle,which helps us to understand the properties of the nonlinear oscillator more profoundly.

Key words: quantum mechanics, nonlinear oscillator, correspondence principle