The effects of the polarization potential serve to model spectra of alkaline atoms. These effects have been known for a long time and notably explained by the physicist Max Born (1926). The experimental knowledge of t...The effects of the polarization potential serve to model spectra of alkaline atoms. These effects have been known for a long time and notably explained by the physicist Max Born (1926). The experimental knowledge of these alkaline spectra enables us to specify the values of these quantum defects. A simple code is used to calculate two quantum defects for which <em>δ<sub>l</sub></em><sub> </sub>can be distinguished as: <em>δ<sub>s</sub></em> <em>l</em> = 0 and <em>δ<sub>p</sub></em> <em>l</em> = 1. On the theoretical part, it is possible to have an analytical expression for these quantum defects <em>δ<sub>l</sub></em>. A second code gives the correct wave functions modified by the quantum defects <em>δ<sub>l</sub></em> with the condition for the principal number: <em>n</em><sub><span style="white-space:nowrap;"><span style="white-space:nowrap;">*</span></span></sub> = <em>n</em> – <em>δ</em><sub><em>l</em></sub> ≥ 1. It is well known that <em>δ</em><sub><em>l</em></sub> → 0 when the kinetic momentum <em>l</em> ≥ 4, and for such momenta the spectra turns out to be hydrogenic. Modern software such as Mathematica, allows us to efficiently generate the polynomes defining wave functions with fractional quantum numbers. This leads to a good theoretical representation of these wave functions. To get numerically the quantum defects, a simple code is given to obtain these quantities when the levels assigned to a transition are known. Then, the quantum defects are inserted into the arguments of the correct modified wave functions for the outer electron of an atom or ion undergoing the short range polarization potential.展开更多
This paper presents the Advanced Observer Model (AOM), a groundbreaking conceptual framework designed to clarify the complex and often enigmatic nature of quantum mechanics. The AOM serves as a metaphorical lens, brin...This paper presents the Advanced Observer Model (AOM), a groundbreaking conceptual framework designed to clarify the complex and often enigmatic nature of quantum mechanics. The AOM serves as a metaphorical lens, bringing the elusive quantum realm into sharper focus by transforming its inherent uncertainty into a coherent, structured ‘Frame Stream’ that aids in the understanding of quantum phenomena. While the AOM offers conceptual simplicity and clarity, it recognizes the necessity of a rigorous theoretical foundation to address the fundamental uncertainties that lie at the core of quantum mechanics. This paper seeks to illuminate those theoretical ambiguities, bridging the gap between the abstract insights of the AOM and the intricate mathematical foundations of quantum theory. By integrating the conceptual clarity of the AOM with the theoretical intricacies of quantum mechanics, this work aspires to deepen our understanding of this fascinating and elusive field.展开更多
The integrable properties of the spheroidal equations are investigated. The shape-invariance property is proved to be retained for the spheroidal equations, for which the recurrence relations are obtained. This is the...The integrable properties of the spheroidal equations are investigated. The shape-invariance property is proved to be retained for the spheroidal equations, for which the recurrence relations are obtained. This is the extension of the recurrence relation of the Legendre polynomials.展开更多
文摘The effects of the polarization potential serve to model spectra of alkaline atoms. These effects have been known for a long time and notably explained by the physicist Max Born (1926). The experimental knowledge of these alkaline spectra enables us to specify the values of these quantum defects. A simple code is used to calculate two quantum defects for which <em>δ<sub>l</sub></em><sub> </sub>can be distinguished as: <em>δ<sub>s</sub></em> <em>l</em> = 0 and <em>δ<sub>p</sub></em> <em>l</em> = 1. On the theoretical part, it is possible to have an analytical expression for these quantum defects <em>δ<sub>l</sub></em>. A second code gives the correct wave functions modified by the quantum defects <em>δ<sub>l</sub></em> with the condition for the principal number: <em>n</em><sub><span style="white-space:nowrap;"><span style="white-space:nowrap;">*</span></span></sub> = <em>n</em> – <em>δ</em><sub><em>l</em></sub> ≥ 1. It is well known that <em>δ</em><sub><em>l</em></sub> → 0 when the kinetic momentum <em>l</em> ≥ 4, and for such momenta the spectra turns out to be hydrogenic. Modern software such as Mathematica, allows us to efficiently generate the polynomes defining wave functions with fractional quantum numbers. This leads to a good theoretical representation of these wave functions. To get numerically the quantum defects, a simple code is given to obtain these quantities when the levels assigned to a transition are known. Then, the quantum defects are inserted into the arguments of the correct modified wave functions for the outer electron of an atom or ion undergoing the short range polarization potential.
文摘This paper presents the Advanced Observer Model (AOM), a groundbreaking conceptual framework designed to clarify the complex and often enigmatic nature of quantum mechanics. The AOM serves as a metaphorical lens, bringing the elusive quantum realm into sharper focus by transforming its inherent uncertainty into a coherent, structured ‘Frame Stream’ that aids in the understanding of quantum phenomena. While the AOM offers conceptual simplicity and clarity, it recognizes the necessity of a rigorous theoretical foundation to address the fundamental uncertainties that lie at the core of quantum mechanics. This paper seeks to illuminate those theoretical ambiguities, bridging the gap between the abstract insights of the AOM and the intricate mathematical foundations of quantum theory. By integrating the conceptual clarity of the AOM with the theoretical intricacies of quantum mechanics, this work aspires to deepen our understanding of this fascinating and elusive field.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10875018 and 10773002)
文摘The integrable properties of the spheroidal equations are investigated. The shape-invariance property is proved to be retained for the spheroidal equations, for which the recurrence relations are obtained. This is the extension of the recurrence relation of the Legendre polynomials.
