aqora

On the unique solution of the quantum mechanical problem of four and more particles. (Comment on a letter by Komarov, Popova and Shablov.)

Bengt R. Karlsson

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoSep 1, 19780 citations

On quantum mechanics of identical particles

Yoshio Ohnuki, S. Kamefuchi

Annals of PhysicsApr 1, 197026 citations

On quantum mechanics of identical particles

Annals of PhysicsMar 1, 19700 citations

Independent subsystems in the problems of few-body interaction. Two-body scattering in force field

Viatcheslav V. Komarov, Anna M. Popova, Vladimir Leonidovich Shablov

A few-body quantum mechanical system is examined. It is assumed that the scattering operator of the system is a sum of two-body potential operators. Some odd ends in the sum commute. Four-dimensional perturbation potentials and second quantized formalism is used for a solution of the problem. The scattering of two distinct particles in a force field is considered as an example. For this case, the system of the integral equations for the scattering amplitudes are obtained. These amplitudes permit us to construct channel Möller operators. It has been shown that such system has unique solution equivalent to the solution of the corresponding Schrödinger equation.A few-body quantum mechanical system is examined. It is assumed that the scattering operator of the system is a sum of two-body potential operators. Some odd ends in the sum commute. Four-dimensional perturbation potentials and second quantized formalism is used for a solution of the problem. The scattering of two distinct particles in a force field is considered as an example. For this case, the system of the integral equations for the scattering amplitudes are obtained. These amplitudes permit us to construct channel Möller operators. It has been shown that such system has unique solution equivalent to the solution of the corresponding Schrödinger equation.

Journal of Mathematical PhysicsApr 1, 19803 citations

Stability of mean-field solutions for collisions

S. Kessal, BERTRAND G. GIRAUD

The time-independent mean-field theory of collisions converts an intractable linear problem, namely, the calculation of the many-body propagator (E-H${)}^{\mathrm{\ensuremath{-}}1}$, into a numerically solvable problem, namely, the coupled calculation of single-particle propagators (\ensuremath{\eta}-h${)}^{\mathrm{\ensuremath{-}}1}$. The latter problem, however, reflects its nonlinearity through many solutions, out of which only one is nonspurious and gives a good approximation to the unique solution (off shell) of the former, linear problem. We prove the stability of this nonspurious solution in the special case of a four-body, one-dimensional collision. The experience thus gained is used to generate transition-shell models in the case of a realistic, three-dimensional, four-body elastic collision.The time-independent mean-field theory of collisions converts an intractable linear problem, namely, the calculation of the many-body propagator (E-H${)}^{\mathrm{\ensuremath{-}}1}$, into a numerically solvable problem, namely, the coupled calculation of single-particle propagators (\ensuremath{\eta}-h${)}^{\mathrm{\ensuremath{-}}1}$. The latter problem, however, reflects its nonlinearity through many solutions, out of which only one is nonspurious and gives a good approximation to the unique solution (off shell) of the former, linear problem. We prove the stability of this nonspurious solution in the special case of a four-body, one-dimensional collision. The experience thus gained is used to generate transition-shell models in the case of a realistic, three-dimensional, four-body elastic collision.

Physical Review AMay 1, 19890 citations

On quantum mechanics of identical particles. II

Yoshio Ohnuki, S. Kamefuchi

Annals of PhysicsJan 1, 19716 citations

On the unique solution of the quantum mechanical problem of four and more particles

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