30 research outputs found
High-Precision Numerical Determination of Eigenvalues for a Double-Well Potential Related to the Zinn-Justin Conjecture
A numerical method of high precision is used to calculate the energy
eigenvalues and eigenfunctions for a symmetric double-well potential. The
method is based on enclosing the system within two infinite walls with a large
but finite separation and developing a power series solution for the
Schrdinger equation. The obtained numerical results are compared with
those obtained on the basis of the Zinn-Justin conjecture and found to be in an
excellent agreement.Comment: Substantial changes including the title and the content of the paper
8 pages, 2 figures, 3 table
Perturbation Theory with a Variational Basis: the Generalized Gaussian Effective Potential
The perturbation theory with a variational basis is constructed and
analyzed.The generalized Gaussian effective potential is introduced and
evaluated up to the second order for selfinteracting scalar fields in one and
two spatial dimensions. The problem of the renormalization of the mass is
discussed in details. Thermal corrections are incorporated. The comparison
between the finite temperature generalized Gaussian effective potential and the
finite temperature effective potential is critically analyzed. The phenomenon
of the restoration at high temperature of the symmetry broken at zero
temperature is discussed.Comment: RevTex, 49 pages, 16 eps figure