The Interacting System

  • John C. Inkson


The calculation of the motion of one particle is, under classical or quantum mechanics, a well-defined problem with a well-defined solution. True, in the latter case we must then be careful as to how we interpret our solution and remember that we work with probabilities, but in principle the solution can be achieved to the Schrödinger equation for that particle. In the usual form we have
$$ H \downarrow = E \downarrow] $$
$$ H = - \frac{{{h^{2}}}}{{2m}}{\nabla ^{2}} + V\left( r \right)] $$
and, with its boundary conditions, it forms a well-defined computational problem. If we consider two or three particles, we may consider the problem soluble whether they have a mutual interaction or not. Once we get into the realm of large numbers of particles, however, sheer computational difficulty prevents a solution. The only exception is the case of a noninteracting set of particles, for then the total Hamiltonian is of the form
$$ H = \sum\limits_{i} { - \frac{{{h^{2}}}}{{2{m_{i}}}}} \nabla _{i}^{2} + V\left( {{r_{i}}} \right)] $$
and splits into a set of independent single-particle Hamiltonians
$$ H = \sum\limits_{i} {{H_{i}}}] $$


Wave Function Dielectric Function Interact System Pauli Principle Trial Wave Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Solid State

  1. Ashcroft, N. W. and Mermin, N. D., Solid State Physics, Holt, Rinehart and Winston, New York, 1976.Google Scholar
  2. Kittel, C., Introduction to Solid State Physics, Wiley, New York, 1971.Google Scholar
  3. Ziman, J. M., Principles of the Theory of Solids, Cambridge University Press, New York, 1969.Google Scholar

Quantum Mechanics

  1. Landau, L. D. and Lifshitz, E. M., Quantum Mechanics, Pergamon, Elmsford: NY, 1977.Google Scholar
  2. Messiah, A., Quantum Mechanics, North Holland, Amsterdam, 1966.Google Scholar
  3. Schiff, L. I., Quantum Mechanics, McGraw-Hill, New York, 1968.Google Scholar

Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • John C. Inkson
    • 1
  1. 1.Cavendish LaboratoryUniversity of CambridgeCambridgeEngland

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