Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Revista Mexicana de Física

Dispersión multinivelar en el espacio de Fock I

Nicolau F. Medina

Published May 10, 2009• 0 citations
OpenAlex

Abstract

IN THE PRESENT PAPER, THE FIRST OF A SERIES, WE DISCUSS THE TIME-DEPENDENT DESCRIPTION OF THE MANY LEVEL SCATTERING. THE INTERACTION IS ASSUMED TO TAKE PLACE THROUGH THE FORMATION OF A COMPOUND NUCLEUS, AND THE DESCRIPTION IS GIVEN IN AN APPROPIATE FOCK SPACE. IN PARTICULAR WE DERIVE IN THIS PAPER THE HAMILTONIAN OF THE PROBLEM ANDE GIVE THE QUANTUM MECHANICAL REPRESENTATION OF POTENTIAL, THIS POTENTIAL HAVING NO CLASSICAL ANALOG.

Related papers

MANY LEVEL SCATTERING IN FOCK SPACE I. II. III

F.M.M. Nicolau

The time-dependent description of the many level scattering is discussed. The interaction is assumed to take place through the formation of a compound nucleus, and the description is given in an appropriate Fock space. In particular the Hamiltonian of the problem is derived and the quantum mechanical representation of the potential is given this potential having no classical analog. (auth)

•Jan 1, 1954•0 citations

Quantum Mechanics in Fock Space

M. Moshińsky

In the present paper we propose to develop a quantum-mechanical scheme in Fock space that would describe interactions that take place through the formation of a compound particle. The discussion will be restricted to a dynamical system representing a single-level scattering process. The state of this dynamical system can be found in two stages: initial particles and compound nucleus. The dynamical behavior of this state will be given in terms of a hamiltonian (that has no classical analog) which will be derived from the boundary conditions satisfied by the state. The representation of the dynamical variables, associated with the two stages of the state, will be discussed, and a complete set of constants of motion of our dynamical system will be given. The expansion of an arbitarary Fock state in terms of the simultaneous eigenstates of this complete set of constants of motion, leads to the generalized Hankel transforms, used in a preceding article for the determination of the time dependent states for scattering and disintegration. In a representation in which the constants of motion are diagonal, the operator representing the relative kinetic energy of the two initial particles will be nondiagonal, particularly in the neighborhood of the resonance energy. The unitary matrix connecting any initial Fock state with the corresponding state at time $t$ will be obtained, and with its help the time-dependent behavior of the Heisenberg dynamical variables of our dynamical system can be derived.

Physical Review•Nov 1, 1951•14 citations

Sobre una clase de transformadas de interés en la dispersión nuclear

M. Moshińsky

THE PRESENT NOTE ANALYSES THE DYNAMICAL DESCRIPTION OF THE SCATTERING DUE TO A SHORT RANGE POTENTIAL. IN PARTICULAR, IT DEVELOPS A CLASS OF TRANSFORMS THAT ARE USEFUL FOR THIS DYNAMICAL DESCRIPTION. A TIME-DEPENDENT GREEN FUNCTION FOR THE SCATTERING PROCESS IS DISCUSSED, THAT TAKES US FROM THE INITIAL STATE (PLANE WAVE) TO THE FINAL STATE (PLANE PLUS SCATTERED WAVES). THIS GREEN FUNCTION CAN BE USED TO GIVER THE MOTION OF ANY WAVE PACKET THAT INITIALLY WAS OUTSIDE THE POTENTIAL. THE PRESENT PAPER COMPLEMENTS A PREVIOUS DYNAMICAL DESCRIPTION OF A SCATTERING PROCESS, IN WHICH THE INTERACTION WAS REPRESENTED BY APPROPRIATE BOUNDARY.

Revista Mexicana de Física•May 10, 2009•1 citation

Condiciones a la frontera y formalismo S de la dispersión nuclear

Manuel Jesús Maldonado Lozano, Nicolau F. Medina

THE PURPOSE OF THE PRESENT IS TO FIND THE RELATION BETWEEN THE S-MATRIX FORMALISM AND THE DESCRIPTION OF INTERACTIONS BY MEANS OF BOUNDARY CONDITIONS. IT IS SHOWN THAT IN THE ABSENCE OF AN ESSENTIAL SINGULARITY AT -- FOR ----, THE DYNAMICAL DESCRIPTION SUGESTED IN A NATURAL WAY BY THE S-FORMALISM, GIVES THE SAME TIME-DEPENDENT WAVE FUNCTIONS THAT ARE OBTAINED WHEN THE INTERACTIONS ARE REPRESENTED BY BOUNDARY CONDITIONS. THE DYNAMICAL DESCRIPTION OF THE S-FORMALISM IS EXTENDED TO THE CASE WHERE ----- MAY HAVE AN ESSENTIAL SINGULARITY AT ---.

Revista Mexicana de Física•May 10, 2009•0 citations

Derivative matrix and scattering matrix

Octavio Cano Corona

THE PRESENT NOTE ANALYSES THE DYNAMICAL DESCRIPTION OF THE SCATTERING DUE TO A SHORT RANGE POTENTIAL. IN PARTICULAR, IT DEVELOPS A CLASS OF TRANSFORMS THAT ARE USEFUL FOR THIS DYNAMICAL DESCRIPTION. A TIME-DEPENDENT GREEN FUNCTION FOR THE SCATTERING PROCESS IS DISCUSSED, THAT TAKES US FROM THE INITIAL STATE (PLANE WAVE) TO THE FINAL STATE (PLANE PLUS SCATTERED WAVES). THIS GREEN FUNCTION CAN BE USED TO GIVER THE MOTION OF ANY WAVE PACKET THAT INITIALLY WAS OUTSIDE THE POTENTIAL. THE PRESENT PAPER COMPLEMENTS A PREVIOUS DYNAMICAL DESCRIPTION OF A SCATTERING PROCESS, IN WHICH THE INTERACTION WAS REPRESENTED BY APPROPRIATE BOUNDARY.

Revista Mexicana de Física•May 10, 2009•0 citations

Descripción dinámica de la dispersión por un potencial

Manuel Jesús Maldonado Lozano

IN THIS PAPER WE GIVE THE TIME DEPENDENT DESCRIPTION OF THE SCATTERING OF A WAVE PACKET BY A SHORT RANGE POTENTIAL. WE SHOW THAT WHEN THE WAVE PACKET IS INITIALLY OUTSIDE THE SCATTERER, IT IS POSIBLE TO INTRODUCE AN APPROPIATE TIME DEPENDENT GREEN FUNCTION TO DESCRIBE THE SCATTERING PROCESS. THIS GREEN FUNCTION WILL BE EVALUATED EXPLICITLY IN TERM OF ERROR INTEGRAL FUNCTIONS, AND THE ONLY PARAMETERS THAT APPEAR IN THE GREEN FUNCTION WILL BE THE POLES OF THE S MATRIX. FROM THE ASYMPTOTIC BEHAVIOR OF THE GREEN FUNCTIOR WHEN T, WE OBTAIN RESTRICIONS ON THE POSITION OF THE POLES OF THE S MATRIX WHICH AGREE WITH THOSE DUE TO THE DEFINITION OF THE S IN TERMS OF THE DERIVATIVE MATRIX R. THE PRESENT ANALYSIS IS CARRIED OUT FOR ARBITRARY ANGULAR MOMENTUM.

Revista Mexicana de Física•May 10, 2009•2 citations
IN THE PRESENT PAPER, THE FIRST OF A SERIES, WE DISCUSS THE TIME-DEPENDENT DESCRIPTION OF THE MANY LEVEL SCATTERING. THE INTERACTION IS ASSUMED TO TAKE PLACE THROUGH THE FORMATION OF A COMPOUND NUCLEUS, AND THE DESCRIPTION IS GIVEN IN AN APPROPIATE FOCK SPACE. IN PARTICULAR WE DERIVE IN THIS PAPER THE HAMILTONIAN OF THE PROBLEM ANDE GIVE THE QUANTUM MECHANICAL REPRESENTATION OF POTENTIAL, THIS POTENTIAL HAVING NO CLASSICAL ANALOG.
In the present paper we propose to develop a quantum-mechanical scheme in Fock space that would describe interactions that take place through the formation of a compound particle. The discussion will be restricted to a dynamical system representing a single-level scattering process. The state of this dynamical system can be found in two stages: initial particles and compound nucleus. The dynamical behavior of this state will be given in terms of a hamiltonian (that has no classical analog) which will be derived from the boundary conditions satisfied by the state. The representation of the dynamical variables, associated with the two stages of the state, will be discussed, and a complete set of constants of motion of our dynamical system will be given. The expansion of an arbitarary Fock state in terms of the simultaneous eigenstates of this complete set of constants of motion, leads to the generalized Hankel transforms, used in a preceding article for the determination of the time dependent states for scattering and disintegration. In a representation in which the constants of motion are diagonal, the operator representing the relative kinetic energy of the two initial particles will be nondiagonal, particularly in the neighborhood of the resonance energy. The unitary matrix connecting any initial Fock state with the corresponding state at time ttt will be obtained, and with its help the time-dependent behavior of the Heisenberg dynamical variables of our dynamical system can be derived.
THE PRESENT NOTE ANALYSES THE DYNAMICAL DESCRIPTION OF THE SCATTERING DUE TO A SHORT RANGE POTENTIAL. IN PARTICULAR, IT DEVELOPS A CLASS OF TRANSFORMS THAT ARE USEFUL FOR THIS DYNAMICAL DESCRIPTION. A TIME-DEPENDENT GREEN FUNCTION FOR THE SCATTERING PROCESS IS DISCUSSED, THAT TAKES US FROM THE INITIAL STATE (PLANE WAVE) TO THE FINAL STATE (PLANE PLUS SCATTERED WAVES). THIS GREEN FUNCTION CAN BE USED TO GIVER THE MOTION OF ANY WAVE PACKET THAT INITIALLY WAS OUTSIDE THE POTENTIAL. THE PRESENT PAPER COMPLEMENTS A PREVIOUS DYNAMICAL DESCRIPTION OF A SCATTERING PROCESS, IN WHICH THE INTERACTION WAS REPRESENTED BY APPROPRIATE BOUNDARY.
THE PURPOSE OF THE PRESENT IS TO FIND THE RELATION BETWEEN THE S-MATRIX FORMALISM AND THE DESCRIPTION OF INTERACTIONS BY MEANS OF BOUNDARY CONDITIONS. IT IS SHOWN THAT IN THE ABSENCE OF AN ESSENTIAL SINGULARITY AT -- FOR ----, THE DYNAMICAL DESCRIPTION SUGESTED IN A NATURAL WAY BY THE S-FORMALISM, GIVES THE SAME TIME-DEPENDENT WAVE FUNCTIONS THAT ARE OBTAINED WHEN THE INTERACTIONS ARE REPRESENTED BY BOUNDARY CONDITIONS. THE DYNAMICAL DESCRIPTION OF THE S-FORMALISM IS EXTENDED TO THE CASE WHERE ----- MAY HAVE AN ESSENTIAL SINGULARITY AT ---.
THE PRESENT NOTE ANALYSES THE DYNAMICAL DESCRIPTION OF THE SCATTERING DUE TO A SHORT RANGE POTENTIAL. IN PARTICULAR, IT DEVELOPS A CLASS OF TRANSFORMS THAT ARE USEFUL FOR THIS DYNAMICAL DESCRIPTION. A TIME-DEPENDENT GREEN FUNCTION FOR THE SCATTERING PROCESS IS DISCUSSED, THAT TAKES US FROM THE INITIAL STATE (PLANE WAVE) TO THE FINAL STATE (PLANE PLUS SCATTERED WAVES). THIS GREEN FUNCTION CAN BE USED TO GIVER THE MOTION OF ANY WAVE PACKET THAT INITIALLY WAS OUTSIDE THE POTENTIAL. THE PRESENT PAPER COMPLEMENTS A PREVIOUS DYNAMICAL DESCRIPTION OF A SCATTERING PROCESS, IN WHICH THE INTERACTION WAS REPRESENTED BY APPROPRIATE BOUNDARY.
IN THIS PAPER WE GIVE THE TIME DEPENDENT DESCRIPTION OF THE SCATTERING OF A WAVE PACKET BY A SHORT RANGE POTENTIAL. WE SHOW THAT WHEN THE WAVE PACKET IS INITIALLY OUTSIDE THE SCATTERER, IT IS POSIBLE TO INTRODUCE AN APPROPIATE TIME DEPENDENT GREEN FUNCTION TO DESCRIBE THE SCATTERING PROCESS. THIS GREEN FUNCTION WILL BE EVALUATED EXPLICITLY IN TERM OF ERROR INTEGRAL FUNCTIONS, AND THE ONLY PARAMETERS THAT APPEAR IN THE GREEN FUNCTION WILL BE THE POLES OF THE S MATRIX. FROM THE ASYMPTOTIC BEHAVIOR OF THE GREEN FUNCTIOR WHEN T, WE OBTAIN RESTRICIONS ON THE POSITION OF THE POLES OF THE S MATRIX WHICH AGREE WITH THOSE DUE TO THE DEFINITION OF THE S IN TERMS OF THE DERIVATIVE MATRIX R. THE PRESENT ANALYSIS IS CARRIED OUT FOR ARBITRARY ANGULAR MOMENTUM.