Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2002-12-23
Physics
Condensed Matter
Strongly Correlated Electrons
75 pages, Lecture notes given at Johannes Kepler Universit\"{a}t-Linz in October and November 2002
Scientific paper
A self-contained pedagogical introduction to the functional Schr\"{o}dinger picture method of many-body theory is given at a level suitable for graduate students and also for many-body physicists who have not been exposed to the functional Schr\"{o}dinger picture method previously. Mathematical tools necessary for the functional Schr\"{o}dinger picture calculation are introduced. The method is first applied to various condensed matter problems including the electron gas, the Hubbard model, the BCS superconductivity, and dilute bose gas within the variational approximation. It is shown that the variational approximation with the Gaussian trial functional invariably leads into the Hartree-Fock results for both zero and finite temperature cases. In order to go beyond the Gaussian results, concepts of variational and optimized perturbation theories are introduced using simple quantum mechanical languages. Then, the variational perturbation theory in the functional Schr\"{o}dinger picture is applied to the $\lambda \phi^4$ model to yield the effective potential to the third order. The optimized perturbation theory is also applied to the $\lambda \phi^4$ model to yield a general expression up to the second order.
Kim Chul Koo
You Sang Koo
No associations
LandOfFree
The Functional Schrödinger Picture Approach to Many-Particle Systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Functional Schrödinger Picture Approach to Many-Particle Systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Functional Schrödinger Picture Approach to Many-Particle Systems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-74399