Optimization of Many-Body Wave Function

A method of calculation of the nuclear reaction matrix is proposed in which the interaction is divided into two parts. The long-range part of the interaction together with the kinetic energy forms the unperturbed Hamiltonian and the short-range interaction is treated as a perturbation. The separation distance is so chosen that the perturbation produces no energy shift, but modifies the many-body wave function. For the special case where the outer part of the interaction is sufficiently weak, a plane-wave approximation is used for the unperturbed wave function, with the result that the diagonal elements of the reaction matrix are given by the first Born approximation of the long-range part of the potential. An iteration scheme is set up to compute the dividing point of the interaction. Such properties of nuclear matter as saturation, binding energy, and rearrangement energy are discussed in terms of the separation distance and its derivatives. Finally, this method is compared with those of Moszkowski and Scott (1960) and Bethe et al. (1963).

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An effective method for generating nonadiabatic many‐body wave function using explicitly correlated Gaussian‐type functions

The Journal of Chemical Physics ◽

10.1063/1.461538 ◽

1991 ◽

Vol 95 (9) ◽

pp. 6681-6698 ◽

Cited By ~ 53

Author(s):

Pawel M. Kozlowski ◽

Ludwik Adamowicz

Keyword(s):

Wave Function ◽

Body Wave ◽

Many Body ◽

Gaussian Type ◽

Explicitly Correlated

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Wave equation for dissipative systems derived from a quantized many-body problem

Canadian Journal of Physics ◽

10.1139/p80-140 ◽

1980 ◽

Vol 58 (7) ◽

pp. 1019-1025 ◽

Cited By ~ 4

Author(s):

M. Razavy

Keyword(s):

Wave Function ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Body Problem ◽

Body Wave ◽

Time Dependent ◽

Dissipative Systems ◽

Many Body ◽

Dependent Part ◽

The Many

A classical many-body problem composed of an infinite number of mass points coupled together by springs is quantized. The masses and the spring constants in this system are chosen in such a way that the motion of each particle is exponentially damped. Because of the quadratic form of the Hamiltonian, the many-body wave function of the system can be written as a product of two terms: a time-dependent phase factor which contains correlations between the classical motions of the particles, and a stationary state solution of the Schrödinger equation. By assuming a Hartree type wave function for the many-particle Schrödinger equation, the contribution of the time-dependent part to the single particle wave function is determined, and it is shown that the time-dependent wave function of each mass point satisfies the nonlinear Schrödinger–Langevin equation. The characteristic decay time of any part of the subsystem, in this model, is related to the stiffness of the springs, and is the same for all particles.

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