All Topics  
Many-body problem

 

 
   Email Print
   Bookmark   Link
 

 

Many-body problem
 
 
  Topics Many-body problem Topic Home

The many-body problem may be defined as the study of the effects of interaction between bodies on the behaviour of a many-body system, i.e. a closed system
Closed system

A closed system is a system in the state of being isolated from its surrounding. It is often used to refer to a theoretical system where perfect closure is an assumption, however in practice no system can be completely closed; there are only varying degrees of closure....
 which does not contain just a few bodies in action, such as the collision
Collision

A collision is an isolated event in which two or more bodies exert relatively strong forces on each other for a relatively short time....
s discussed in classical mechanics
Classical mechanics

Classical mechanics is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies....
. Due to the number of particles/bodies contained in such a system, the number of degrees of freedom increases rapidly, and it becomes difficult to describe the mechanics of the system by using a small system of equations.

The many-body problem is usually posed in quantum mechanics
Quantum mechanics

Quantum mechanics is a set of principles underlying the most fundamental known description of all physical systems at the microscopic scale . Notable amongst these principles are both a dual wave-like and particle-like behavior of matter and radiation, and prediction of probabilities in situations where classical physics predicts certaintie...
 as the question of solving for more complex problems than the hydrogen atom
Hydrogen atom

A hydrogen atom is an atom of the chemical element hydrogen. The Electric charge neutral atom contains a single positively-charged proton and a single negatively-charged electron bound to the nucleus by the Coulomb force....
.






Discussion
Ask a question about 'Many-body problem'
Start a new discussion about 'Many-body problem'
Answer questions from other users
Full Discussion Forum



Encyclopedia


The many-body problem may be defined as the study of the effects of interaction between bodies on the behaviour of a many-body system, i.e. a closed system
Closed system

A closed system is a system in the state of being isolated from its surrounding. It is often used to refer to a theoretical system where perfect closure is an assumption, however in practice no system can be completely closed; there are only varying degrees of closure....
 which does not contain just a few bodies in action, such as the collision
Collision

A collision is an isolated event in which two or more bodies exert relatively strong forces on each other for a relatively short time....
s discussed in classical mechanics
Classical mechanics

Classical mechanics is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies....
. Due to the number of particles/bodies contained in such a system, the number of degrees of freedom increases rapidly, and it becomes difficult to describe the mechanics of the system by using a small system of equations.

The many-body problem is usually posed in quantum mechanics
Quantum mechanics

Quantum mechanics is a set of principles underlying the most fundamental known description of all physical systems at the microscopic scale . Notable amongst these principles are both a dual wave-like and particle-like behavior of matter and radiation, and prediction of probabilities in situations where classical physics predicts certaintie...
 as the question of solving for more complex problems than the hydrogen atom
Hydrogen atom

A hydrogen atom is an atom of the chemical element hydrogen. The Electric charge neutral atom contains a single positively-charged proton and a single negatively-charged electron bound to the nucleus by the Coulomb force....
. Depending on the complexity of the molecule, different models are used. For example, a many-body problem posed for a polymer
Polymer

A polymer is a large molecule composed of repeating structural units typically connected by covalent chemical bonds. While polymer in popular usage suggests plastic, the term actually refers to a large class of natural and synthetic materials with a variety of properties....
 molecule would be different from a single polyatomic molecule. The former might include some statistical parameters, whereas the latter would likely exclude these.

Approaches

In some many-body problems, the solutions are chaotic
Chaos theory

In mathematics, chaos theory describes the behavior of certain dynamical system s ? that is, systems whose states evolve with time ? that may exhibit dynamics that are highly sensitive to initial conditions ....
. Sometimes, many-body problems can be simplified by canonicalization
Canonicalization

In computer science, canonicalization is a process for converting data that has more than one possible representation into a "standard" canonical representation....
.

Another approach to solve many-body problems is to simply ignore some interactions within the system. This allows the many-body problem to be reduced to a simpler problem, often a set of smaller, independent and easier to solve problems.

Quotes


See also

  • Hartree-Fock
    Hartree-Fock

    In computational physics and computational chemistry, the Hartree-Fock method is an approximate method for the determination of the Stationary state wavefunction and Stationary state energy of a Many-body problem....
     approximation
  • The helium atom
  • Density functional theory
    Density functional theory

    Density functional theory is a quantum mechanics theory used in physics and chemistry to investigate the electronic structure of Many-body problem, in particular atoms, molecules, and the condensed phases....


Further reading

  • Stephen Jenkins:
  • D. J. Thouless
    David Thouless

    David J. Thouless is a condensed matter physicist and Wolf Prize winner.Thouless earned his PhD at Cornell University under Hans Bethe. He was a professor of mathematical physics at Birmingham University in the United Kingdom before becoming a professor of physics at the University of Washington in Seattle in 1980....
    : The quantum mechanics of many-body systems. New York, Academic Press, 1972, ISBN 0-12-691560-1.