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

Apple Academic Press eBooks

Introductory Theory of Scattering

Nelson Enrique Bolivar, Gabriel Abellán

Published May 23, 2018• 0 citations
Publisher

Abstract

The theory of scattering consists in studying the collision also called dispersion, between two or more particles. This chapter studies the simplest case of the collision between two particles without spin. Historically, the discovery of the quantum world and the particles was made by studying collision processes. Many physics experiments are based on collisions, or more precisely of scattering. In 2012 particle physicists announced the long awaited discovery of the Higgs Boson in the collision processes at the Large Hadron Collider (LHC). An incoming spherical wave does not correspond to an usual experimental situation. In an experimental situation, the incoming wave is more often modeled by an incident plane wave.

DOI
10.1201/9781351166287-14

Related papers

Scattering theory

Giampiero V. M. Esposito, Giuseppe Marmo, Gennaro Miele +1 more

Aims and problems of quantum scattering theory Scattering theory is the branch of physics concerned with interacting systems on a scale of time and/or distance that is large compared with the scale of the interaction itself, and it provides the most powerful tool for studying the microscopic nature of the world. In quantum mechanics, a typical scattering process involves a beam of particles prepared with a given energy and with a more or less defined linear momentum. One then studies either the collision with a similar wave packet, or the collision of the given wave packet against a fixed target. In particular, for a two-body elastic scattering problem with conservative forces, we work in the centre of mass frame, hence reducing the original problem to the analysis of a particle in an external field of forces. Indeed, in Section 7.2 we already used such a technique in the investigation of the hydrogen atom. The crucial difference with respect to Section 7.2 is that, in scattering problems, the continuous spectrum and its perturbations are studied, whereas the Balmer formula has to do with bound states. In the following section we outline the basic aspects of what is called time-dependent scattering. Time-dependent scattering The physical situation we would like to study is as follows: a beam of particles is prepared in a state that is approximately free and allowed to evolve towards the scatterer. After the collision we detect the scattered beam far away from the interaction region.

Cambridge University Press eBooks•Oct 31, 2014•0 citations

Scattering Theory

Lukong Cornelius Fai

The scattering process is equivalent to the collision process and relates the physics of gaseous states, solid state physics (electrons colliding with phonons in the crystal lattice), plasma physics and so on. When we cannot directly visualize particles, scattering can be a valuable probe for their study. An example is the hydrogen atom that scattering experiments confirm it to have a nucleus with an electron orbiting around it. Scattering experiments also confirm protons to have some constituents called quarks. So the scattering theory is pivotal in understanding of the quantum nature of particles. In principle, we can formulate all problems of quantum mechanics in the language of scattering theory.

CRC Press eBooks•Apr 19, 2022•0 citations

Scattering

Asim Gangopadhyaya, Constantin Rasinariu

There are several ways of gathering experimental evidence about microscopic systems. Spectral analysis gives information about the bound states of the system, while scattering experiments probe their inner structure. Rutherford's pioneering alpha scattering experiments yielded the first glimpse into the structure of atoms. Such experiments opened the door to modern collider experiments, allowing us to peer deeper into the structure of matter. In this chapter, we will study only elastic collisions, in which the nature of the scattered particles does not change. This is expected for low energies in the non-relativistic regime. We first introduce the concept of cross-section and then study two complementary approaches to scattering: the Born approximation, which is suitable when the energy of the incoming particles is high in comparison with the potential energy of the target, and the partial waves method, which applies best when the two energies are comparable.

CRC Press eBooks•Jul 28, 2025•0 citations

The quantum mechanical theory of collisions

Roy J. Glauber

The Quantum Mechanical Theory of Collis3ions. I»-In the present course we shall consider the quantum mechanical treatment of problems of particle interactions in which at least one of the particles is unbound and therefore able to travel large distances freely.In effect such particles are able to communicate the results of their interaction directly to macroscopic detection apparatus* The interpretation of the resulting data is in general the most direct way of forming conclusions about the interactions.A considerable variety of physical phenomena involves unbound particles» Among the simplest are scattering processes ;in particular the deflection of particles from a collinated beam.More general collision processes which induce reactions of various sorts also lie within the class we shall examine, Our chief concern willbe with the means of solving problems in which well-defined models have been postulated to describe the basic interactions.We shall restrict ourselves, in fact, to the treatment of fairly simple models, and shall discuss a number of approaches to the problems they raise.We begin by discussing the scattering of particles by a simple potential field, fixed in space» The problem of two free particles with a potential between them of course assumes this form in the center-of-mass system.By imagining that a beam of particles of constant strenght is at all times being scattered by the potential, we cay seek to describe the situation with the stationary-state Schrb'dinger equation.

•Jan 1, 1954•0 citations

Scattering Theory I

Nandita Rudra

In a collision problem, the energy of the incident particle is specified in advance, unlike the bound state case where the boundary conditions on the wavefunctions at large distances give rise to the quantization of energy into discrete energy levels of the system. In the scattering problems the behaviour of the wavefunction at large distances is obtained in terms of the energy of the incident particle. We discuss some of the simpler theories in this chapter, deferring some of the formal theories for the next chapter.

CRC Press eBooks•Aug 19, 2019•0 citations

Hybrid Quantum Computing Apocalypse

Robert Skopec

Chinese scientists won a major victory, by proving that the Majorana fermion-a particle we've found tantaliying hints for years-genuinely exists.This discovery has huge implications for quantum computing, and it might change the world.Don Lincoln, a senior physicist at Fermilab, does research using the Large Hadron Collider.He is the author of "The Large Hadron Collider: The Extraordinary Story of the Higgs Boson and Other Stuff That Will Blow Your Mind" and produces a series of science education videos.To the question: Why is there (in our Universe) something including cancer, rather than nothing?He is giving the simplest scientific answer: We shouldn't exist at all.

Biomedical Journal of Scientific & Technical Research•Sep 21, 2018•3 citations
The theory of scattering consists in studying the collision also called dispersion, between two or more particles. This chapter studies the simplest case of the collision between two particles without spin. Historically, the discovery of the quantum world and the particles was made by studying collision processes. Many physics experiments are based on collisions, or more precisely of scattering. In 2012 particle physicists announced the long awaited discovery of the Higgs Boson in the collision processes at the Large Hadron Collider (LHC). An incoming spherical wave does not correspond to an usual experimental situation. In an experimental situation, the incoming wave is more often modeled by an incident plane wave.
Aims and problems of quantum scattering theory Scattering theory is the branch of physics concerned with interacting systems on a scale of time and/or distance that is large compared with the scale of the interaction itself, and it provides the most powerful tool for studying the microscopic nature of the world. In quantum mechanics, a typical scattering process involves a beam of particles prepared with a given energy and with a more or less defined linear momentum. One then studies either the collision with a similar wave packet, or the collision of the given wave packet against a fixed target. In particular, for a two-body elastic scattering problem with conservative forces, we work in the centre of mass frame, hence reducing the original problem to the analysis of a particle in an external field of forces. Indeed, in Section 7.2 we already used such a technique in the investigation of the hydrogen atom. The crucial difference with respect to Section 7.2 is that, in scattering problems, the continuous spectrum and its perturbations are studied, whereas the Balmer formula has to do with bound states. In the following section we outline the basic aspects of what is called time-dependent scattering. Time-dependent scattering The physical situation we would like to study is as follows: a beam of particles is prepared in a state that is approximately free and allowed to evolve towards the scatterer. After the collision we detect the scattered beam far away from the interaction region.
The scattering process is equivalent to the collision process and relates the physics of gaseous states, solid state physics (electrons colliding with phonons in the crystal lattice), plasma physics and so on. When we cannot directly visualize particles, scattering can be a valuable probe for their study. An example is the hydrogen atom that scattering experiments confirm it to have a nucleus with an electron orbiting around it. Scattering experiments also confirm protons to have some constituents called quarks. So the scattering theory is pivotal in understanding of the quantum nature of particles. In principle, we can formulate all problems of quantum mechanics in the language of scattering theory.
There are several ways of gathering experimental evidence about microscopic systems. Spectral analysis gives information about the bound states of the system, while scattering experiments probe their inner structure. Rutherford's pioneering alpha scattering experiments yielded the first glimpse into the structure of atoms. Such experiments opened the door to modern collider experiments, allowing us to peer deeper into the structure of matter. In this chapter, we will study only elastic collisions, in which the nature of the scattered particles does not change. This is expected for low energies in the non-relativistic regime. We first introduce the concept of cross-section and then study two complementary approaches to scattering: the Born approximation, which is suitable when the energy of the incoming particles is high in comparison with the potential energy of the target, and the partial waves method, which applies best when the two energies are comparable.
The Quantum Mechanical Theory of Collis3ions. I»-In the present course we shall consider the quantum mechanical treatment of problems of particle interactions in which at least one of the particles is unbound and therefore able to travel large distances freely.In effect such particles are able to communicate the results of their interaction directly to macroscopic detection apparatus* The interpretation of the resulting data is in general the most direct way of forming conclusions about the interactions.A considerable variety of physical phenomena involves unbound particles» Among the simplest are scattering processes ;in particular the deflection of particles from a collinated beam.More general collision processes which induce reactions of various sorts also lie within the class we shall examine, Our chief concern willbe with the means of solving problems in which well-defined models have been postulated to describe the basic interactions.We shall restrict ourselves, in fact, to the treatment of fairly simple models, and shall discuss a number of approaches to the problems they raise.We begin by discussing the scattering of particles by a simple potential field, fixed in space» The problem of two free particles with a potential between them of course assumes this form in the center-of-mass system.By imagining that a beam of particles of constant strenght is at all times being scattered by the potential, we cay seek to describe the situation with the stationary-state Schrb'dinger equation.
In a collision problem, the energy of the incident particle is specified in advance, unlike the bound state case where the boundary conditions on the wavefunctions at large distances give rise to the quantization of energy into discrete energy levels of the system. In the scattering problems the behaviour of the wavefunction at large distances is obtained in terms of the energy of the incident particle. We discuss some of the simpler theories in this chapter, deferring some of the formal theories for the next chapter.
Chinese scientists won a major victory, by proving that the Majorana fermion-a particle we've found tantaliying hints for years-genuinely exists.This discovery has huge implications for quantum computing, and it might change the world.Don Lincoln, a senior physicist at Fermilab, does research using the Large Hadron Collider.He is the author of "The Large Hadron Collider: The Extraordinary Story of the Higgs Boson and Other Stuff That Will Blow Your Mind" and produces a series of science education videos.To the question: Why is there (in our Universe) something including cancer, rather than nothing?He is giving the simplest scientific answer: We shouldn't exist at all.