Variational method for the double-well anharmonic oscillator

The independent-minimization variational method is extended to cases with more than one variational parameter and applied to the anharmonic-oscillator problem. The results, including estimates of the tunneling effect, are reasonable. For the double-well potential the method provides a criterion to decide, given the coupling parameter $\lambda$, up to which energy level a classical broken-symmetry solution is present. Above that level the symmetry is restored. A lower bound for the value of $\lambda$ allowing for symmetry-broken solutions is also obtained.