scholarly journals Selected topics in the large quantum number expansion

Author(s):  
Luis Alvarez-Gaume ◽  
Domenico Orlando ◽  
Susanne Reffert
2003 ◽  
Vol 81 (7) ◽  
pp. 929-939
Author(s):  
James D Bonnar ◽  
Jeffrey R Schmidt

Classical trajectories for the Coulomb potential are obtained from the large principle quantum-number limit of solutions to the nonrelativistic Schrödinger equation, by use of integral equations satisfied by the radial probability density function. These trajectories are found to be in excellent agreement with those computed directly from classical mechanics, in accordance with a statement of the Bohr Correspondence principle, except in a region very close to the center of force. PACS No.: 05.45.Mt


1926 ◽  
Vol 23 (4) ◽  
pp. 403-411 ◽  
Author(s):  
Bertha Swirles

If it is assumed that the series electron of an atom polarises the core, then it has been shown by Born and Heisenberg that the polarisability α of the core in a given state may be calculated from the corresponding term value by means of the approximate formulae, where q is the quantum defect, δν is the difference between the term and the corresponding hydrogen term, R is the Rydberg constant in cm.−1, α1 is the radius of first hydrogen orbit, n is the principal quantum number, k is the azimuthal quantum number, For terms with small quantum defect either of the formulae (1) and may be used, but for terms with large quantum defect (1) gives a higher degree of accuracy.


2021 ◽  
Vol 103 (2) ◽  
Author(s):  
Henri Lehec ◽  
Xin Hua ◽  
Pierre Pillet ◽  
Patrick Cheinet

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
H. Hassanabadi ◽  
E. Maghsoodi ◽  
Akpan N. Ikot ◽  
S. Zarrinkamar

Spin and pseudospin symmetries of Dirac equation are solved under scalar and vector generalized isotonic oscillators and Cornell potential as a tensor interaction for arbitrary quantum number via the analytical ansatz approach. The spectrum of the system is numerically reported for typical values of the potential parameters.


1994 ◽  
Vol 27 (6) ◽  
pp. 2197-2211 ◽  
Author(s):  
A J Bracken ◽  
G F Melloy
Keyword(s):  

2012 ◽  
Vol 90 (2) ◽  
pp. 230-236 ◽  
Author(s):  
Ningjiu Zhao ◽  
Yufang Liu

In this work, we employed the quasi-classical trajectory (QCT) method to study the vector correlations and the influence of the reagent initial rotational quantum number j for the reaction He + T2+ (v = 0, j = 0–3) → HeT+ + T on a new potential energy surface (PES). The PES was improved by Aquilanti co-workers (Chem. Phys. Lett. 2009. 469: 26–30). The polarization-dependent differential cross sections (PDDCSs) and the distributions of P(θr), P([Formula: see text]r), and P(θr, [Formula: see text]r) are presented in this work. The plots of the PDDCSs provide us with abundant information about the distribution of the product angular momentum polarization. The P(θr) is used to describe the correlation between k (the relative velocity of the reagent) and j′ (the product rotational angular momentum). The distribution of dihedral angle P([Formula: see text]r) shows the k–k′–j′ (k′ refers to the relative velocity of the product) correlation. The PDDCS calculations illustrate that the product of this reaction is mainly backward scatter and it has the strongest polarization in the backward and sideways scattering directions. At the same time, the results of the P([Formula: see text]r) demonstrate that the product HeT+ tends to be oriented along the positive direction of the y axis and it tends to rotate right-handedly in planes parallel to the scattering plane. Moreover, the distribution of the P(θr) manifests that the product angular momentum is aligned along different directions relative to k. The direction of the product alignment may be perpendicular, opposite, or parallel to k. Moreover, our calculations are independent of the initial rotational quantum number.


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