Hilbert space, orbital wave functions

In a true scattering problem, an incident wave is specified, and scattered wave components of ifr are varied. In MST or KKR theory, the fixed term x in the full Lippmann-Schwinger equation, f = x + / GqVms required to vanish, x is a solution of the Helmholtz equation. In each local atomic cell r of a space-filling cellular model, any variation of i// in the orbital Hilbert space induces an infinitesimal variation of the KR functional of the form 8 A = fr Govi/s) + he. This... 

The OOA, also known as Kugel-Khomskii approach, is based on the partitioning of a coupled electron-phonon system into an electron spin-orbital system and crystal lattice vibrations. Correspondingly, Hilbert space of vibronic wave functions is partitioned into two subspaces, spin-orbital electron states and crystal-lattice phonon states. A similar partitioning procedure has been applied in many areas of atomic, molecular, and nuclear physics with widespread success. It s most important advantage is the limited (finite) manifold of orbital and spin electron states in which the effective Hamiltonian operates. For the complex problem of cooperative JT effect, this partitioning simplifies its solution a lot. 

Quantum mechanics involves the characterization of a physical system by a set of Hermitian operators, one for any observable quantity, in a state space S assumed to be a Hilbert space. In Schrodinger s perspective, S was viewed as a space of complex wave functions with differential operators as tools. In this sense, the operator characterizing the energy of the system, the Hamilton operator H, was one of the most important. However, linear momentum P, coordinated spatial positions Q, rotational (orbital) momentum L, the square of the total momentum L2, and the spin J of... 

To do so we compare the APSG wave function (67) with a wave function Wr in which only the spin-orbital pair ro. r is substituted, but with the substitution limited to the subspace of Hilbert space associated with r. The wave function Wr can then also be written in the APSG form (69), where the geminals cos for S i are Slater determinants built up from the spin orbitals s , It is convenient to expand the geminals in their natural form (71). In terms of the natural orbitals Papsg and Wr have the following Cl expansions respectively ... 

---