Exact Solutions to the Dirac Equation for a Coulomb Potential in D + 1 Dimensions

Gu, Xiaochen; Zhong, Qi; Dong, Shi‐Hai

doi:10.1142/s0218301302000879

Cited by 50 publications

(57 citation statements)

References 21 publications

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“…[44]), though we will not need the explicit expressions here. To proceed further, we separate variables by making an ansatz for solutions of the Dirac equationψ…”

Section: Discussionmentioning

confidence: 99%

Supersymmetric multi-trace boundary conditions in AdS

Amsel¹,

Marolf²

2009

Class. Quantum Grav.

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Boundary conditions for massive fermions are investigated in AdS d for d ≥ 2. For fermion masses in the range 0 ≤ |m| < 1/2ℓ with ℓ the AdS length, the standard notion of normalizeability allows a choice of boundary conditions. As in the case of scalars at or slightly above the BreitenlohnerFreedman (BF) bound, such boundary conditions correspond to multi-trace deformations of any CFT dual. By constructing appropriate boundary superfields, for d = 3, 4, 5 we identify joint scalar/fermion boundary conditions which preserve either N = 1 supersymmetry or N = 1 superconformal symmetry on the boundary. In particular, we identify boundary conditions corresponding via AdS/CFT (at large N ) to a 595-parameter family of double-trace marginal deformations of the low-energy theory of N M2-branes which preserve N = 1 superconformal symmetry. We also establish that (at large N and large 't Hooft coupling λ) there are no marginal or relevant multi-trace deformations of 3+1 N = 4 super Yang-Mills which preserve even N = 1 supersymmetry. Contents

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“…[44]), though we will not need the explicit expressions here. To proceed further, we separate variables by making an ansatz for solutions of the Dirac equationψ…”

Section: Discussionmentioning

confidence: 99%

Supersymmetric multi-trace boundary conditions in AdS

Amsel¹,

Marolf²

2009

Class. Quantum Grav.

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“…Chen [26] obtained the exact solutions of N -dimensional harmonic oscillator via Laplace transformation. Recent works in mathematical physics have been reported: The algebraic method in which group theory approach has been used in an arbitrary D-dimensional space by [18,27,55,56,65,67], supersymmetry approach in an arbitrary D-dimensional space by [65,66,68,106], quantum gravity theories in extra dimensions by [8,17,81].…”

mentioning

confidence: 99%

“…Furthermore, the study of the Schrödinger equation with certain central physical potentials in D dimensions has become an important aspect in Quantum Mechanics, however, such a problem has been extended to the relativistic equation case by [31,34,55,56]. Dong [30] applied a suitable ansatz to obtain the solutions of the D-dimensional radial Schrödinger equation with some anharmonic potentials.…”

mentioning

confidence: 99%

Exactly Complete Solutions of the Pseudoharmonic Potential in N-Dimensions

2007

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We present analytically the exact solutions of the Schrödinger equation in the N -dimensional spaces for the pseudoharmonic oscillator potential by means of the ansatz method. The energy eigenvalues of the bound states are easily calculated from this eigenfunction ansatz. The normalized wavefunctions are also obtained. A realization of the ladder operators for the wavefunctions is studied and we deduced that these operators satisfy the commutation relations of the generators of the dynamical group SU (1, 1). Some expectation values for r −2 , r 2 , T , V , H , p 2 and the virial theorem for the pseudoharmonic oscillator potential in an arbitrary number of dimensions are obtained by means of the Hellmann-Feynman theorems. Each solution obtained is dimensions and parameters dependent.

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“…where the last equality holds for l > 1, and N D,l denotes the normalization factor given in [37]. The product of two spherical harmonic polynomials Y m ′ (ŷ) belongs to the direct product of two representation (l) and (l ′ ), which is a reducible representation.…”

Section: The Generalized Spherical Harmonic Polynomialsmentioning

confidence: 99%