Level-Dependent New Tamm-Dancoff Method

The coefficients of the Wick expansion relating ordinary operator products to normal products define the transformation taking the single-time Tamm-Dancoff $\tau$-function recursion equation into the new Tamm-Dancoff (NTD) $\phi$-function recursion equations. It is shown that the $\phi$-function transformation can be constructed from the ground-state $\tau$-function recursion system for the harmonic oscillator, and that an infinite number of other energy-level-dependent transformations can be constructed in the same way. The latter allow for the development of a level-dependent NTD method permitting the accurate determination of transition frequencies through an accumulative level-by-level procedure, assuming knowledge of the ground-state energy. For the sample systems considered, the procedure is self-contained and self-consistent, the ground-state energy can be determined within the context of the NTD method. Numerical results are obtained for several one-dimensional nonlinear oscillators.