The use of quadratic forms in the calculation of ground state electronic structures
- Departamento de Fisica y Quimica Teorica, Facultad de Quimica, Universidad Nacional Autonoma de Mexico, AP 70-528, 04510, Mexico D.F. (Mexico)
There are many examples in theoretical physics where a fundamental quantity can be considered a quadratic form {rho}={sigma}{sub i}{rho}{sub i}=vertical bar {psi} vertical bar{sup 2} and the corresponding linear form {psi}={sigma}{sub i}{psi}{sub i} is highly relevant for the physical problem under study. This, in particular, is the case of the density and the wave function in quantum mechanics. In the study of N-identical-fermion systems we have the additional feature that {psi} is a function of the 3N configuration space coordinates and {rho} is defined in three-dimensional real space. For many-electron systems in the ground state the wave function and the Hamiltonian are to be expressed in terms of the configuration space (CS), a replica of real space for each electron. Here we present a geometric formulation of the CS, of the wave function, of the density, and of the Hamiltonian to compute the electronic structure of the system. Then, using the new geometric notation and the indistinguishability and equivalence of the electrons, we obtain an alternative computational method for the ground state of the system. We present the method and discuss its usefulness and relation to other approaches.
- OSTI ID:
- 20860768
- Journal Information:
- Journal of Mathematical Physics, Vol. 47, Issue 8; Other Information: DOI: 10.1063/1.2229423; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
Similar Records
Concerning the nature of the lambda-transition order parameter
Time dependence, complex scaling, and the calculation of resonances in many-electron systems. [Wave functions, energies, widths]