The Relativistic Screened Coulomb plus Ringed-Shaped-Like Potential via Shape-Invariance Approach

AbstractThe bound-state solutions of the Dirac equation for the screened Coulomb potential plus a ringshaped- like potential are determined using supersymmetry quantum mechanics and invariance method for arbitrary angular momentum state J. In the calculations, a proper approximate scheme for the centrifugal term is proposed and the un-normalized eigenfunctions are obtained in terms of the hypergeometric functions.

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Direct measurement of a 27-dimensional orbital-angular-momentum state vector

Nature Communications ◽

10.1038/ncomms4115 ◽

2014 ◽

Vol 5 (1) ◽

Cited By ~ 129

Author(s):

Mehul Malik ◽

Mohammad Mirhosseini ◽

Martin P. J. Lavery ◽

Jonathan Leach ◽

Miles J. Padgett ◽

...

Keyword(s):

Angular Momentum ◽

Direct Measurement ◽

Orbital Angular Momentum ◽

State Vector ◽

Momentum State ◽

Angular Momentum State

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Possible dual bubble-like structure predicted by the relativistic Hartree–Bogoliubov model

International Journal of Modern Physics E ◽

10.1142/s0218301320500731 ◽

2020 ◽

Vol 29 (09) ◽

pp. 2050073

Author(s):

Sven Åberg ◽

Akhilesh Yadav ◽

A. Shukla

Keyword(s):

Angular Momentum ◽

Nuclear Structure ◽

Experimental Observation ◽

Mass Region ◽

Momentum State ◽

Angular Momentum State ◽

Shell Gaps

Experimental observation of [Formula: see text]Si as a proton bubble nuclei has heated up the interest in the study of exotic bubble shaped nuclei. In this work, some of the potential doubly bubble-like (for proton as well as neutron both simultaneously) cases have been explored using relativistic Hartree–Bogoliubov (RHB) in light mass region, specially around N or [Formula: see text]. Further, the role of pairing and the evolution of new shell gaps around [Formula: see text] or [Formula: see text] and 34 have been investigated, as one moves toward drip lines. This study suggests that the occupancies/vacancies of neutron/proton orbitals for lower angular momentum state plays major role in nuclear structure to create bubble-like structure and [Formula: see text]O[Formula: see text], [Formula: see text]Mg8 and [Formula: see text]Si[Formula: see text] may have dual bubble-like structures.

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Demonstration of Orbital Angular Momentum State Conversion using Two Hybrid 3D Photonic Integrated Circuits

Optical Fiber Communication Conference ◽

10.1364/ofc.2014.th4a.1 ◽

2014 ◽

Cited By ~ 7

Author(s):

Chuan Qin ◽

Binbin Guan ◽

Ryan Scott ◽

Roberto Proietti ◽

Nicolas K. Fontaine ◽

...

Keyword(s):

Angular Momentum ◽

Integrated Circuits ◽

Orbital Angular Momentum ◽

Photonic Integrated Circuits ◽

Momentum State ◽

Angular Momentum State ◽

Two Hybrid

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ARBITRARY l-WAVE BOUND STATE SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH THE ECKART POTENTIAL

Modern Physics Letters B ◽

10.1142/s0217984909020424 ◽

2009 ◽

Vol 23 (18) ◽

pp. 2269-2279 ◽

Cited By ~ 10

Author(s):

YONG-FENG DIAO ◽

LIANG-ZHONG YI ◽

TAO CHEN ◽

CHUN-SHENG JIA

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Approximation Scheme ◽

Function Analysis ◽

Bound State ◽

Centrifugal Term ◽

Radial Wave ◽

Shape Invariance ◽

Eckart Potential ◽

Analytical Results

By using a modified approximation scheme to deal with the centrifugal term, we solve approximately the Schrödinger equation for the Eckart potential with the arbitrary angular momentum states. The bound state energy eigenvalues and the unnormalized radial wave functions are approximately obtained in a closed form by using the supersymmetric shape invariance approach and the function analysis method. The numerical experiments show that our analytical results are in better agreement with those obtained by using the numerical integration approach than the analytical results obtained by using the conventional approximation scheme to deal with the centrifugal term.

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