a New Equations of Motion Linearization Scheme: Application to the Heisenberg and Hubbard Hamiltonians.

Morton D. Kostin

Pavel Pokhilko, Anna I. Krylov

Effective Hamiltonians, which are commonly used for fitting experimental observables, provide a coarse-grained representation of exact many-electron states obtained in quantum chemistry calculations; however, the mapping between the two is not trivial. In this contribution, we apply Bloch's formalism to equation-of-motion coupled-cluster wave functions to rigorously derive effective Hamiltonians in Bloch's and des Cloizeaux's forms. We report the key equations and illustrate the theory by application to systems with two or three unpaired electrons, which give rise to electronic states of covalent and ionic characters. We show that Hubbard's and Heisenberg's Hamiltonians can be extracted directly from the so-obtained effective Hamiltonians. By establishing a quantitative connection between many-body states and simple models, the approach facilitates the analysis of the correlated wave functions. We propose a simple diagnostic for assessing the validity of the model space choice based on the overlaps between the target- and model-space states. Artifacts affecting the quality of electronic structure calculations such as spin contamination are also discussed.

G.R.W. Quispel, Hans W. Capel

Fardin Kheirandish, Majid Amooshahi

The electromagnetic field in a linear absorptive dielectric medium is quantized in the framework of the damped polarization model by a new minimal coupling scheme. A Hamiltonian containing a reservoir with continuous degrees of freedom is proposed. The reservoir minimally couples to the dielectric polarization and the electromagnetic field. The Langevin equation is obtained as the equation of motion of the polarization field. Finally, the equations of motion are solved for homogeneous dielectrics.

Ching‐Teh Li

Based on an equations-of-motion method in the framework of Heisenberg's matrix mechanics, we investigate the conditions under which a one-dimensional quantum mechanical system becomes exactly solvable. By linearizing the equation of motion which is a double-commutation relation of some appropriately chosen function of the position operator with the Hamiltonian, we obtained a set of nontrivial exactly solvable potentials in one dimension. These potentials not only can be solved analytically in closed forms but also contain both the Morse potential and the Poschl-Teller potential as their limiting cases. They may thus be valuable for some potential model calculations as well as for testing various approximation schemes. We also examine these potentials in the framework of supersymmetric quantum mechanics, which is particularly useful for studying exactly solvable potentials.