Several quantum mechanical theories and statistical and field theoretic models of physical interest possess continuous group symmetry often in some internal space. Many of these theories admit straightforward extensions in which the number of internal degrees of freedom N may be treated as a free variable parameter. Inflating the given number N to infinity then entails, quite surprisingly, a drastic simplification in the analyses of a diverse class of such theories. The method of large-N expansion hinges on the fact that if the large-N limit of such a problem can be obtained explicitly then the finite-N corrections can be incorporated by introducing a systematic expansion in powers of 1/N and contact with the original theory may be made by substituting for N its given fixed value at the end of the calculation. This inverse-N expansion technique has emerged in recent years as a powerful approximation scheme in fields as disparate as quantum mechanics, nuclear physics, critical phenomena, laser physics and quantum chromodynamics [1,2]. Here we shall however restrict our discussion mainly to quantum mechanics where the large-N expansion was first applied by Ferrei and Scalapino  in 1974 and since then interest in this subject has continued unabated.
KeywordsGround State Energy Critical Phenomenon Helium Atom Angular Momentum Quantum Number Generalize Coherent State
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