Large-N expansions in quantum mechanics, atomic physics and some O(N) invariant systems

Chatterjee, Ashok

doi:10.1016/0370-1573(90)90048-7

Cited by 205 publications

(119 citation statements)

References 135 publications

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“…x is a Ddimensional position vector with hyperspherical Cartesian components 1 2 · · · D given as follows 1 [71][72][73][74][75][76][77][78][79]:…”

Section: The Klein-gordon Equation With Equal Scalar and Vector Potenmentioning

confidence: 99%

Relativistic solution in D-dimensions to a spin-zero particle for equal scalar and vector ring-shaped Kratzer potential

Ikhdair¹,

Sever

2008

Open Physics

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“…x is a Ddimensional position vector with hyperspherical Cartesian components 1 2 · · · D given as follows 1 [71][72][73][74][75][76][77][78][79]:…”

Section: The Klein-gordon Equation With Equal Scalar and Vector Potenmentioning

confidence: 99%

Relativistic solution in D-dimensions to a spin-zero particle for equal scalar and vector ring-shaped Kratzer potential

Ikhdair¹,

Sever

2008

Open Physics

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“…Hence we show the semiclassical nature of the large N approximation (59). Corrections to the result of the large N limit for the finite N case may be obtained by incorporating in the theory the quantum fluctuations around the classical minimum [20].…”

Section: Large N Limitmentioning

confidence: 99%

Equivalent linear two-body method for many-body problems

Kim

Zubarev

1999

J. Phys. B: At. Mol. Opt. Phys.

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This paper reports a detailed description of the equivalent linear two-body method for the many body problem, which is based on an approximate reduction of the many-body Schrödinger equationby the use of a variational principle. To test the accuracy of the method it has been applied to the one-dimensional N-body problem with pair-wise contact interactions (McGurie-Yang N-body problem) and to the dilute Bose-Einstein condensation (BEC) of atoms in harmonic traps at zero temperature. For both cases, it is shown that the method gives excellent results for

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“…x is a D-dimensional position vector with the hyperspherical Cartesian components 1 2 · · · D given as follows 1 [30,31,[91][92][93][94][95][96]:…”

Section: Exact Solutions Of the Quantum Systemmentioning

confidence: 99%

“…The unit vector along x is usually denoted by x = x/ Additionally, the angular momentum operators L 2 are defined as [30,31,[91][92][93][94][95][96]: The substitution of Eqs. (15) and (17)- (19) into Eq.…”

Section: Exact Solutions Of the Quantum Systemmentioning

confidence: 99%

Exact solutions of the D-dimensional Schrödinger equation for a ring-shaped pseudoharmonic potential

Ikhdair¹,

Sever

2008

Open Physics

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Abstract:A new non-central potential, consisting of a pseudoharmonic potential plus another recently proposed ringshaped potential, is solved. It has the formThe energy eigenvalues and eigenfunctions of the bound-states for the Schrödinger equation in D-dimensions for this potential are obtained analytically by using the Nikiforov-Uvarov method. The radial and angular parts of the wave functions are obtained in terms of orthogonal Laguerre and Jacobi polynomials. We also find that the energy of the particle and the wave functions reduce to the energy and the wave functions of the bound-states in three dimensions. PACS

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Large-N expansions in quantum mechanics, atomic physics and some O(N) invariant systems

Cited by 205 publications

References 135 publications

Relativistic solution in D-dimensions to a spin-zero particle for equal scalar and vector ring-shaped Kratzer potential

Relativistic solution in D-dimensions to a spin-zero particle for equal scalar and vector ring-shaped Kratzer potential

Equivalent linear two-body method for many-body problems

Exact solutions of the D-dimensional Schrödinger equation for a ring-shaped pseudoharmonic potential

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