body system
- This article is about the many-body problem in quantum mechanics. For the n-body problem in classical mechanics, see n-body problem.
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Contents
- 1 Definition
- 2 Example
- 3 Quotes
- 4 See also
- 5 References and further reading
- 6 External links
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Definition
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 which does not contain just a few bodies in action, such as the collisions discussed in classical mechanics. Due to the amount of particles/bodies contained in such a system, the number of degrees of freedom increase rapidly, and it becomes difficult to describe the mechanics of the system by using a small system of equations.
In some many body problems, the solutions are chaotic. Sometimes, many body problems can be simplified by Canonicalization.
Another approach to solve many body problems is to simply ignore some interactions that are 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.
The many-body problem is usually posed in quantum mechanics, as the question of solving for more complex problems than the hydrogen atom. Depending on the complexity of the molecule, different models are used. For example, a many body problem posed for a polymer molecule would be different from a single polyatomic molecule. The former might include some statistical parameters, whereas the latter would likely exclude these.
Example
Solving the Molecular Hamiltonian for a particular chemical system is an example of a many body problem.
Quotes
- "It would indeed be remarkable if Nature fortified herself against further advances in knowledge behind the analytical difficulties of the many-body problem."
- - Max Born, 1960
See also
- Hartree-Fock approximation
References and further reading
- Jenkins, Stephen. "3. The Many Body Problem and Density Functional Theory". Many Body Problem and Density Functional Theory
- D. J. Thouless, "The quantum mechanics of many-body systems", 2d ed., New York, Academic Press, 1972. ISBN 0-12-691560-1
- D. J. Thouless, "The quantum mechanics of many-body systems", New York, Academic Press, 1961. LCCN 61012282 /L/r842
External links
- Evidence for Efimov quantum states in an ultracold gas of Cs atoms
Categories: Quantum mechanics | Quantum physics stubs
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