  We construct a generalised expression for the normal ordering of
(a+a^{\dagger})^{m} for integral values of m and use the result to study the
quantum anharmonic oscillator problem in the Heisenberg approach. In
particular, we derive generalised expressions for energy eigen values and
frequency shifts for the Hamiltonian
H=\frac{x^{2}}{2}+\frac{\dot{x}^{2}}{2}+\frac{\lambda}{m}x^{m}. We also derive
a closed form first order multi scale perturbation theoretic operator solution
of this Hamiltonian with a view to generalise some recent results of Bender and
Bettencourt .
