scholarly journals Energy Spectrum for a Short-Range 1/r Singular Potential with a Non-Orbital Barrier Using the Asymptotic Iteration Method

2016 ◽  
Vol 04 (01) ◽  
pp. 79-85 ◽  
Author(s):  
Abdullah J. Sous ◽  
Abdulaziz D. Alhaidari
Keyword(s):  
Energy Spectrum ◽  
Iteration Method ◽  
Short Range ◽  
Singular Potential ◽  
Asymptotic Iteration Method

scholarly journals ASYMPTOTIC ITERATION METHOD FOR SINGULAR POTENTIALS

2008 ◽  
Vol 23 (09) ◽  
pp. 1405-1415 ◽  
Author(s):  
BRODIE CHAMPION ◽  
RICHARD L. HALL ◽  
NASSER SAAD
Keyword(s):  
Wave Function ◽  
Efficient Method ◽  
Iteration Method ◽  
Singular Potential ◽  
Asymptotic Form ◽  
Iteration Process ◽  
Asymptotic Iteration Method ◽  
Singular Potentials ◽  
Radial Schrödinger Equation ◽  
Arbitrary Dimensions

The asymptotic iteration method (AIM) is applied to obtain highly accurate eigenvalues of the radial Schrödinger equation with the singular potential V(r) = r2+λ/rα(α,λ>0) in arbitrary dimensions. Certain fundamental conditions for the application of AIM, such as a suitable asymptotic form for the wave function, and the termination condition for the iteration process, are discussed. Several suggestions are introduced to improve the rate of convergence and to stabilize the computation. AIM offers a simple, accurate, and efficient method for the treatment of singular potentials, such as V(r), valid for all ranges of coupling λ.

scholarly journals Colloidal CdSe nanocrystals are inherently defective

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Tamar Goldzak ◽  
Alexandra R. McIsaac ◽  
Troy Van Voorhis
Keyword(s):  
Charge Transfer ◽  
Energy Spectrum ◽  
Surface Structure ◽  
Short Range ◽  
Surface Defects ◽  
Low Energy ◽  
Lewis Base ◽  
Cdse Nanocrystals ◽  
Photoinduced Charge Transfer ◽  
Photoinduced Charge

AbstractColloidal CdSe nanocrystals (NCs) have shown promise in applications ranging from LED displays to medical imaging. Their unique photophysics depend sensitively on the presence or absence of surface defects. Using simulations, we show that CdSe NCs are inherently defective; even for stoichiometric NCs with perfect ligand passivation and no vacancies or defects, we still observe that the low energy spectrum is dominated by dark, surface-associated excitations, which are more numerous in larger NCs. Surface structure analysis shows that the majority of these states involve holes that are localized on two-coordinate Se atoms. As chalcogenide atoms are not passivated by any Lewis base ligand, varying the ligand should not dramatically change the number of dark states, which we confirm by simulating three passivation schemes. Our results have significant implications for understanding CdSe NC photophysics, and suggest that photochemistry and short-range photoinduced charge transfer should be much more facile than previously anticipated.

On the single-particle-energy spectrum of a Λ particle in nuclear matter

1970 ◽  
Vol 48 (23) ◽  
pp. 2804-2808 ◽  
Author(s):  
K. F. Chong ◽  
Y. Nogami ◽  
E. Satoh
Keyword(s):  
Energy Spectrum ◽  
Nuclear Matter ◽  
Single Particle ◽  
Short Range ◽  
Particle Energy ◽  
Pair Approximation ◽  
Single Particle Energy ◽  
Short Range Repulsion ◽  
Separable Potentials ◽  
Independent Pair

The single-particle-energy spectrum of a Λ particle in nuclear matter is examined in the independent-pair approximation, by assuming nonlocal separable potentials for the ΛN interaction. Effects of short-range repulsion in the ΛN interaction on the Λ binding are also examined in terms of separable potentials of rank two.

scholarly journals THE ENERGY EIGENVALUES OF THE TWO DIMENSIONAL HYDROGEN ATOM IN A MAGNETIC FIELD

2006 ◽  
Vol 15 (06) ◽  
pp. 1263-1271 ◽  
Author(s):  
A. SOYLU ◽  
O. BAYRAK ◽  
I. BOZTOSUN
Keyword(s):  
Magnetic Field ◽  
Hydrogen Atom ◽  
Iteration Method ◽  
Weak Magnetic Field ◽  
The Other ◽  
Asymptotic Iteration Method ◽  
Iterative Approach ◽  
Two Dimensional ◽  
Energy Eigenvalues ◽  
The Magnetic Field

In this paper, the energy eigenvalues of the two dimensional hydrogen atom are presented for the arbitrary Larmor frequencies by using the asymptotic iteration method. We first show the energy eigenvalues for the case with no magnetic field analytically, and then we obtain the energy eigenvalues for the strong and weak magnetic field cases within an iterative approach for n=2-10 and m=0-1 states for several different arbitrary Larmor frequencies. The effect of the magnetic field on the energy eigenvalues is determined precisely. The results are in excellent agreement with the findings of the other methods and our method works for the cases where the others fail.

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