The paper presents a circular scale of time—and its diagrams—which can be successfully applied in calculating the Schr<span style="white-space:nowrap;">ö</span>dinger perturbation ener...The paper presents a circular scale of time—and its diagrams—which can be successfully applied in calculating the Schr<span style="white-space:nowrap;">ö</span>dinger perturbation energy of a non-degenerate quantum state. This seems to be done in a more simple way than with the aid of any other of the perturbation approaches of a similar kind. As an example of the theory suitable to comparison is considered the Feynman diagrammatic method based on a straight-linear scale of time which represents a much more complicated formalism than the present one. All diagrams of the approach outlined in the paper can obtain as their counterparts the algebraic formulae which can be easily extended to an arbitrary Schr<span style="white-space:nowrap;">ö</span>dinger perturbation order. The calculations and results descending from the perturbation orders <em>N</em> between <em>N</em> = 1 and <em>N </em>= 7 are reported in detail.展开更多
The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eige...The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.展开更多
Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics. Their an...Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics. Their analytic ground eigenvalues and eigenfunctions are obtained by means of a series in low frequency. The ground eigenvalue and eigenfunction for small complex frequencies are numerically determined.展开更多
In this paper, we report some results about the effects of varying the wavelength in a structure of a non-holographic fiber specklegram sensor. In these arrangements, the speckle pattern produced by a multi-mode optic...In this paper, we report some results about the effects of varying the wavelength in a structure of a non-holographic fiber specklegram sensor. In these arrangements, the speckle pattern produced by a multi-mode optical fiber is coupled to the asingle-mode optical fiber with lower numerical aperture, which produces a filtering effect that can be used as an optical transduction mechanism. The influence of the wavelength on the sensor performance is evaluated by changing the laser wavelength, and a strong effect on the linearity and reproducibility of its response is found. Lasers emitting at 1310nm, 1550nm, and 1625nm are used.展开更多
文摘The paper presents a circular scale of time—and its diagrams—which can be successfully applied in calculating the Schr<span style="white-space:nowrap;">ö</span>dinger perturbation energy of a non-degenerate quantum state. This seems to be done in a more simple way than with the aid of any other of the perturbation approaches of a similar kind. As an example of the theory suitable to comparison is considered the Feynman diagrammatic method based on a straight-linear scale of time which represents a much more complicated formalism than the present one. All diagrams of the approach outlined in the paper can obtain as their counterparts the algebraic formulae which can be easily extended to an arbitrary Schr<span style="white-space:nowrap;">ö</span>dinger perturbation order. The calculations and results descending from the perturbation orders <em>N</em> between <em>N</em> = 1 and <em>N </em>= 7 are reported in detail.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10875018 and 10773002)
文摘The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10875018 and 10773002)
文摘Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics. Their analytic ground eigenvalues and eigenfunctions are obtained by means of a series in low frequency. The ground eigenvalue and eigenfunction for small complex frequencies are numerically determined.
文摘In this paper, we report some results about the effects of varying the wavelength in a structure of a non-holographic fiber specklegram sensor. In these arrangements, the speckle pattern produced by a multi-mode optical fiber is coupled to the asingle-mode optical fiber with lower numerical aperture, which produces a filtering effect that can be used as an optical transduction mechanism. The influence of the wavelength on the sensor performance is evaluated by changing the laser wavelength, and a strong effect on the linearity and reproducibility of its response is found. Lasers emitting at 1310nm, 1550nm, and 1625nm are used.
