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Science China Technological Sciences

Study on spectral structure of quantum remote sensing

BI Si-wen, Han Jixia

Published Jan 1, 2006• 5 citations
OpenAlex

Abstract

A study of the use of fine spectral structure in quantum remote sensing, including an expression, begins with a summary of present-day applications of spectrum remote sensing, which is followed by a theoretical discussion of the influence of electronic spin upon hydrogen-like atom energy levels and the calculation of spectral line in the absence of a circumstance field.

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Science China Technological Sciences•Jan 1, 2006•4 citations
A study of the use of fine spectral structure in quantum remote sensing, including an expression, begins with a summary of present-day applications of spectrum remote sensing, which is followed by a theoretical discussion of the influence of electronic spin upon hydrogen-like atom energy levels and the calculation of spectral line in the absence of a circumstance field.
At the beginning of 2001, Professor Siwen Bi first proposed the new direction of quantum remote sensing at home and abroad. Based on the research of fundamental theory and information mechanism of quantum remote sensing, a new concept of quantum spectral imaging was put forward in August 2006. 10 years, quantum spectral imaging research has made breakthrough progress and stage results. Firstly, the research status of spectral imaging and the background of quantum spectrum imaging are introduced. Secondly, the concept and research methods of quantum spectrum imaging, the relationship between quantum spectrum imaging and spectral imaging and advantages are introduced. The basic theory of quantum spectroscopy is described, especially the research of quantum spectroscopy imaging and quantum spectroscopy. Finally, the significance and application prospect of quantum spectrum imaging are described.
Niels Bohr’s model of the hydrogen and hydrogen-like atoms, in which the electron is allowed to revolve in certain circular orbits around the nucleus, was extended by Arnold Sommerfeld to allow for the possibility of elliptical orbits. Each elliptical orbit was constrained by two quantization conditions specified by a positive integer nφ and a non-negative integer nr. If, in the presence of the attractive Coulomb force between the electron and the nucleus, the dynamics of the atom were taken to be governed by the Newtonian laws of motion, the energy Ɛ of the two-particle system was found to be a function of the positive integer n = nr + nφ. The atomic energy levels thus exhibited an n-fold degeneracy, which would be lifted in the presence of external electric or magnetic fields, thus accounting for the fine-structure of the spectral lines emitted by the atom—phenomena observed, respectively, in the Stark effect and the Zeeman effect. Sommerfeld also examined the behavior of his elliptical orbits by allowing the revolving electron to obey Einstein’s relativistic dynamics. In this case, the energy-level degeneracies were lifted (even in the absence of external perturbations), and the elliptical orbits were found to precess around the nucleus—similarly to the precession of, say, the orbit of the planet Mercury around the Sun. What is astonishing about Sommerfeld’s relativistic expression of the energy Ɛ as a function of nφ and nr is that it is precisely the same expression as obtained for hydrogen and hydrogen-like atoms from Dirac’s equation, which came more than a decade later. Recall that the spin of the electron was not yet discovered when Sommerfeld developed his model, and that in Dirac’s fully-relativistic quantum mechanics, the spectral fine-structure arises from the coupling of the electron’s spin to its orbital motion. The present paper provides a streamlined yet detailed account of Sommerfeld’s elliptical orbits in hopes of bringing about a deeper appreciation for the miraculous coincidence of Sommerfeld’s result with that derived from Dirac’s equation.