Energy eigenstates of spherically symmetric potentials using the shifted<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:mfrac></mml:math>expansion

Imbo, Tom D.; Pagnamenta, A.; Sukhatme, U.

doi:10.1103/physrevd.29.1669

Cited by 200 publications

(160 citation statements)

References 21 publications

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“…Up to this point, one would conclude that the above procedure is nothing but an imitation of the eminent shifted large-N expansion (SLNT) [12,14,16,[20][21][22]. However, because of the limited capability of SLNT in handling largeorder corrections via the standard Rayleigh-Schrödinger perturbation theory, only low-order corrections have been reported, sacrificing in effect its preciseness.…”

Section: The Methodsmentioning

confidence: 99%

Anharmonic oscillators energies via artificial perturbation method

Mustafa

Odeh

2000

Eur. Phys. J. B

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Section: The Methodsmentioning

confidence: 99%

Anharmonic oscillators energies via artificial perturbation method

Mustafa

Odeh

2000

Eur. Phys. J. B

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“…Indeed, in spite of an amazing universality of all the different 1/ℓ (better known as 1/N) expansion techniques (cf. a small sample of the relevant computational tricks in [28]), one usually finds and returns to the common harmonic oscillator H (HO) 0 ≡ H (q=0) , in spite of the wealth and variability of the underlying physics [29]. For this reason we recently started to study some alternative possibilities offered by the QES models [17,20].…”

Section: Discussionmentioning

confidence: 99%

New exact solutions for polynomial oscillators in large dimensions

Znojil

Yanovich

Gerdt

2003

J. Phys. A: Math. Gen.

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A new type of exact solvability is reported. Schrödinger equation is considered in a very large spatial dimension D ≫ 1 and its central polynomial potential is allowed to depend on "many" (= 2q) coupling constants. In a search for its bound states possessing an exact and elementary wave functions ψ (proportional to a harmonicoscillator-like polynomial of a freely varying, i.e., not just small, degree N), the "solvability conditions" are known to form a complicated nonlinear set which requires a purely numerical treatment at a generic choice of D, q and N. Assuming that D is large we discovered and demonstrate that this problem may be completely factorized and acquires an amazingly simple exact solution at all N and up to q = 5 at least.

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“…The last two terms on the right-hand side of eq. (197) are just cyclic permutations of the first. Henceforth, such terms occuring in any potential are referred to as "cyclic terms".…”

Section: Shape Invariance and 3-body Solvable Potentialsmentioning

confidence: 99%

“…A slightly modified, physically motivated approach, called the "shifted large-N method" [196,197,198,199] incorporates exactly known analytic results into 1/N expansions, greatly enhancing their accuracy, simplicity and range of applicability. In this subsection, we will descibe how the rate of convergence of shifted 1/N expansions can be still further improved by using the ideas of SUSY QM [77].…”

Section: Supersymmetry and Large-n Expansionsmentioning

confidence: 99%

Parasupersymmetry in quantum mechanics

Khare

1993

Journal of Mathematical Physics

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In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable and an array of powerful new approximation methods for handling potentials which are not exactly solvable. In this report, we review the theoretical formulation of supersymmetric quantum mechanics and discuss many applications. Exactly solvable potentials can be understood in terms of a few basic ideas which include supersymmetric partner potentials, shape invariance and operator transformations. Familiar solvable potentials all 1 have the property of shape invariance. We describe new exactly solvable shape invariant potentials which include the recently discovered self-similar potentials as a special case. The connection between inverse scattering, isospectral potentials and supersymmetric quantum mechanics is discussed and multi-soliton solutions of the KdV equation are constructed. Approximation methods are also discussed within the framework of supersymmetric quantum mechanics and in particular it is shown that a supersymmetry inspired WKB approximation is exact for a class of shape invariant potentials. Supersymmetry ideas give particularly nice results for the tunneling rate in a double well potential and for improving large N expansions. We also discuss the problem of a charged Dirac particle in an external magnetic field and other potentials in terms of supersymmetric quantum mechanics. Finally, we discuss structures more general than supersymmetric quantum mechanics such as parasupersymmetric quantum mechanics in which there is a symmetry between a boson and a para-fermion of order p.

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Energy eigenstates of spherically symmetric potentials using the shifted1Nexpansion

Cited by 200 publications

References 21 publications

Anharmonic oscillators energies via artificial perturbation method

Anharmonic oscillators energies via artificial perturbation method

New exact solutions for polynomial oscillators in large dimensions

Parasupersymmetry in quantum mechanics

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