Application of the VFM to One-Dimensional Systems with Trivial Boundary Conditions

Abstract

Let us consider a 2K- anharmonic oscillator, defined by the Hamiltonian

$$H\left( g,\lambda \right)={{P}^{2}}+g{{x}^{2}}+\lambda {{x}^{2K}};K=2,3,\ldots ,\lambda >0$$

(23.1)

which, due to the Symanzik Theorem /1/, satisfies the unitary equivalence relationship (Appendix A)

$$H\left( g,\lambda \right)={{\lambda }^{1/\left( K+1 \right)}}H\left( g{{\lambda }^{-2/\left( K+1 \right)}},1 \right)$$

(23.2)

.