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The relativistic feature of Hydrogen-like atoms in the Heisenberg picture
  • J Jahanpanah,
  • A Vahedi,
  • H . Khosrojerdi
J Jahanpanah
Kharazmi University

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A Vahedi
Kharazmi University
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H . Khosrojerdi
Kharazmi University
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The relativistic properties of Hydrogen-like atoms (HLAs) are here investigated in the Heisenberg picture for the first time. The relativistic vibrational Hamiltonian (RVH) is first defined as a power series of harmonic oscillator Hamiltonian by using the relativistic energy eigenvalue . By applying the first-order RVH (proportional to ) to the Heisenberg equation, a pair of coupled equations is turned out for the relativistic motion of the electron’s position and linear momentum. A simple comparison of the first-order relativistic and nonrelativistic equations reveals this reality that the natural (fundamental) frequency of HLA (like entropy) is slowly raised by increasing the atomic number from . The second-order RVH (proportional to ) has then been implemented to determine an exact expression for the electron relativistic frequency in the different atomic energy levels. In general, the physical role of RVH is fundamental because it not only specifies the temporal relativistic variations of position, velocity, and linear momentum of the oscillating electron, but also identifies the corresponding relativistic potential, kinetic, and mechanical energies. The results will finally be testified by demonstrating energy conservation.
16 Oct 2021Submitted to International Journal of Quantum Chemistry
25 Oct 2021Submission Checks Completed
25 Oct 2021Assigned to Editor
26 Oct 2021Reviewer(s) Assigned
12 Nov 2021Review(s) Completed, Editorial Evaluation Pending
12 Nov 2021Editorial Decision: Revise Major
17 Dec 20211st Revision Received
20 Dec 2021Assigned to Editor
20 Dec 2021Submission Checks Completed
20 Dec 2021Reviewer(s) Assigned
19 Feb 2022Review(s) Completed, Editorial Evaluation Pending
21 Feb 2022Editorial Decision: Revise Minor
28 Feb 20222nd Revision Received
02 Mar 2022Submission Checks Completed
02 Mar 2022Assigned to Editor
02 Mar 2022Reviewer(s) Assigned
23 Mar 2022Review(s) Completed, Editorial Evaluation Pending
23 Mar 2022Editorial Decision: Accept