Optimized perturbation method for the propagation in the anharmonic   oscillator potential
  The application of the optimized expansion for the quantum-mechanical propagation in the anharmonic potential $\lambda x^4$ is discussed for real and imaginary time. The first order results in the imaginary time formalism provide approximations to the free energy and particle density which agree well with the exact results in the whole range of temperatures. 
Anna Okopi\'nska