The Tamm–Dancoff approximation or simple particle-hole theory

Roberto C. Bochicchio, Horacio Grinberg

Behram N. Kurșunoǧlu

Richard R. Chasman

A method is presented for the treatment of particle-hole residual interactions that is both simple and extremely accurate. This method is compared with the random-phase approximation, Tamm-Dancoff approximation, and other approximations in the schematic model of Brown and the monopole model of Lipkin, Meshkov, and Glick.

B. P. Nigam

The Tamm-Dancoff approximation is applied to the interaction Hamiltonian used by Bogoliubov in his theory of superconductivity. It is shown that (i) the requirement that there is no virtual production of a single pair of electron and hole without phonons, or (ii) the electron-phonon coupling parameter tends to zero, leads to essentially the same compensating equation as obtained by Bogoliubov.

Seiya Nishiyama, Hiroyuki Morita, Hiromasa Ohnishi

The traditional Tamm–Dancoff (TD) method is one of the standard procedures for solving the Schrödinger equation of fermion many-body systems. However, it meets a serious difficulty when an instability occurs in the symmetry-adapted ground state of the independent particle approximation (IPA) and when the stable IPA ground state becomes of broken symmetry. If one uses the stable but broken symmetry IPA ground state as the starting approximation, TD wave functions also become of broken symmetry. On the contrary, if we start from a symmetry-adapted but unstable wave function, the convergence of the TD expansion becomes bad. Thus, the requirements of symmetry and rapid convergence are not in general compatible in the conventional TD expansion of the systems with strong collective correlations. Along the same line as Fukutome's, we give a group-theoretical deduction of a U ( n ) dyadic TD equation by using a matrix-valued generator coordinate.