Geometric phase in relativistic quantum theory

A review on the use of DFT for the prediction of the properties of nanomaterials

“…To solve the complex Schrödinger equation, several approximations were developed such as Born-Oppenheimer approximation. [5][6][7] In 1964, Hohenberg and Kohn have postulated two theorems that served as fundamentals of DFT. 5 The rst theorem states that in a system having n interacting electrons, the many-body ground state wavefunction (J n. r n ) of all electrons is a unique function of the electronic density (r(r)).…”

Sub-Geometric Phases in Density Matrices

“…Generally, geometric phase was investigated by the Schrödinger equation. However, it can also be studied by the path integral formalism 5 and relativistic Dirac equation 6 . Herein, a different method was used.…”

Berry phase generation and measurement in a single trapped ion

“…Geometric phases in general and Berry phase in particular has been studied for a variety of physical systems and conditions [9][10][11][12]. The theoretical treatment of geometric phases has been generalized for composite systems having internal structure particularly in the light of quantum optics [13].…”