A new technique for deriving the large-N solution of the Klein-Gordon equation

Stepanov, S. S.; Tutik, R. S.

doi:10.1088/0305-4470/24/9/004

Cited by 6 publications

(13 citation statements)

References 12 publications

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“…which was formerly applied in deriving coefficients of the 1/N expansions [26][27][28][29]. In the limiting case, ash → 0, a particle is now lowered to the bottom of a potential well and its classical energy becomes E cl = minV (x) , which equals to zero in our case.…”

Section: Methodsmentioning

confidence: 88%

Semiclassical treatment of logarithmic perturbation theory

Dobrovolska¹,

Tutik²

1999

J. Phys. A: Math. Gen.

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Abstract. The explicit semiclassical treatment of logarithmic perturbation theory for the nonrelativistic bound states problem is developed. Based uponh-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions for the one-dimensional anharmonic oscillator is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and exited states have been obtained. As an example, the perturbation expansions for the energy eigenvalues of the harmonic oscillator perturbed by λx 6 are considered.

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Section: Methodsmentioning

confidence: 88%

Semiclassical treatment of logarithmic perturbation theory

Dobrovolska¹,

Tutik²

1999

J. Phys. A: Math. Gen.

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“…This condition is exact and is widely used for deriving the high-order corrections to the WKB-approximation [20] and the 1/N-expansions [8,9]. Now one important detail must be noted.…”

Section: The Methodsmentioning

confidence: 99%

“…At that time the semiclassical 1/N-expansion, being complementary to the WKBmethod, requires the conditions [8,9] h → 0, n = const, l → ∞,h n → 0,h l = const.…”

Section: The Methodsmentioning

confidence: 99%

“…A number of such approaches to solving the radial Klein-Gordon equation in analytical expressions have been developed, including, in particular, the use of the relativistic hypervirial and Hellmann-Feynman theorems [1], the 1/N-expansions [2][3][4][5][6][7][8][9], the method of Regge trajectories [10][11][12], the elements of an SO(2, 1) Lie algebra [13,14] and a perturbation scheme based on a comparison equation [15].…”

Section: Introductionmentioning

confidence: 99%

“…If the WKBapproach is realized using the rule,h → 0, n → ∞, l → ∞,hn = const,hl = const, application of the conditionh → 0, n = const, l → ∞,hn → 0,hl = const was proved to lead to the method of 1/N-expansion [8,9] and the method of Regge trajectories [11,12]. Here we address ourselves to the alternative possibility:h → 0, n = const, l = const,hn → 0,hl → 0, that results in the explicit semiclassical treatment of the logarithmic perturbation theory for the radial Klein-Gordon equation.…”

Section: Introductionmentioning

confidence: 99%

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Logarithmic Perturbation Theory for Radial Klein–gordon Equation With Screened Coulomb Potentials via ℏ-Expansions

Dobrovolska

Tutik

2004

Int. J. Mod. Phys. A

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Abstract. The explicit semiclassical treatment of logarithmic perturbation theory for the bound-state problem within the framework of the radial Klein-Gordon equation with attractive real-analytic screened Coulomb potentials, contained time-component of a Lorentz four-vector and a Lorentz-scalar term, is developed. Based upon h-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and excited states have been obtained. As an example, the perturbation expansions for the energy eigenvalues for the Hulthén potential containing the vector part as well as the scalar component are considered.

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Shifted 1/N Expansion Within the Framework of the SO(2,1) Pseudo-spin Formalism

Mukhopadhyay¹,

Chatterjee

2010

Int J Theor Phys

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The shifted 1/N expansion is organized within the framework of the SO(2, 1) pseudo-spin formalism and the method is formulated to derive the ground state energies of a class of power law potentials.Keywords Shifted large-N expansion · Pseudo-spin formalism · Power-law potentialsThe method of large-N expansion has won acceptance as a powerful non-perturbative approach in quantum mechanics, atomic physics, statistical mechanics and field theory (for a review see [1][2][3][4][5][6][7]). Notwithstanding its proven efficacy in dealing with a wide variety of problems the method is at times plagued with slow convergence. To improve the situation, Sukhatme and Imbo [33] have developed the so called shifted 1/N expansion scheme introducing an extra degree of freedom, called the shift parameter. Sukhatme and collaborators [34] have given a prescription for the choice of the shift parameter which is physically motivated and developed their theory in the framework of the perturbed oscillator technique. The shifted 1/N expansion method [33] has been used by several authors with overwhelming success [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]. There have also been several other formulations [50-54] to obtain improved convergence in the 1/N expansion.In the present paper we have made an attempt to introduce the idea of the shifted 1/N expansion of Sukhatme and Imbo [34] in a wider framework namely in the pseudo-spin formulation [55,56]. It is well-known that the pseudo-spin formalism is a very powerful and versatile technique which finds applications in various branches of physics [57-60] and therefore it is expected that the shifted 1/N expansion in the pseudo-spin formalism would have a much wider applicability. We shall formulate the theory for a class of spherically symmetric potentials and compare the results with those obtained by Sukhatme and Imbo [33] with the perturbed oscillator method.

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A new technique for deriving the large-N solution of the Klein-Gordon equation

Cited by 6 publications

References 12 publications

Semiclassical treatment of logarithmic perturbation theory

Semiclassical treatment of logarithmic perturbation theory

Logarithmic Perturbation Theory for Radial Klein–gordon Equation With Screened Coulomb Potentials via ℏ-Expansions

Shifted 1/N Expansion Within the Framework of the SO(2,1) Pseudo-spin Formalism

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