Is there any unique frequency operator for quantum-mechanical anharmonic oscillators

We discuss some recently proposed methods that yield operator solutions free from secular terms for the quantum-mechanical anharmonic oscillators. The frequency operators obtained in those methods are not same. In the present work we show that the apparent differences between the frequency operators derived by different approaches are due to the different ordering of noncommuting observables. Here we derive some relations between the existing frequency operators. In some cases we generalize results from quartic to higher anharmonicities. (c) 2005 Elsevier B.V All rights reserved.