A New Method for the Energy Eigenstates of Anharmonic Oscillators

A new interpolative approximation method is devised for obtaining the eigenvalues and eigenfunctions of anharmonic oscillators. The method is applied to the one-dimensional quartic anharmonic oscillator. The eigenvalues and eigenfunctions are obtained explicitly in the lowest order of approximation. The results are compared with those from other methods. The eigenvalues are found to deviate from the exact values by less than 0.5% for large values of the anharmonic coefficient. Further possible generalisations and higher levels of approximations are also discussed.