The identity and the supersymmetry shape invariance for a class of exponential-type molecule potentials are studied by introducing a deformed five-parameter exponential-type potential (DFPEP) and via the multi-paramet...The identity and the supersymmetry shape invariance for a class of exponential-type molecule potentials are studied by introducing a deformed five-parameter exponential-type potential (DFPEP) and via the multi-parameter deformations. It has been shown that the DFPEP is a shape-invariant potential with a translation of parameters. By making use of the shape invariance approach, the exact energy levels are determined for the bound states with zero angular momentum. A class of molecule potentials and their exact energy spectra for the zero angular momentum states are reduced from the DFPEP and a general energy spectrum formula, respectively. The interrelations for some molecule potentials are also discussed.展开更多
The dissociation energy and equilibrium bond length as explicit parameters are used to establish an improved five-parameter exponential-type potential energy model for diatomic molecules. We demonstrate that the five-...The dissociation energy and equilibrium bond length as explicit parameters are used to establish an improved five-parameter exponential-type potential energy model for diatomic molecules. We demonstrate that the five-parameter exponential-type potential is identical to the Tietz potential for diatomic molecules. It is observed that the improved five-parameter exponential-type potential can well model the internuclear interaction potential energy curve for the ground electronic state of the carbon monoxide molecule by the utilization of the experimental values of three molecular constants.展开更多
We obtain the quantized momentum eigenvalues, <em>P<sub>n</sub></em>, and the momentum eigenstates for the space-like Schrodinger equation, the Feinberg-Horodecki equation, with the improved de...We obtain the quantized momentum eigenvalues, <em>P<sub>n</sub></em>, and the momentum eigenstates for the space-like Schrodinger equation, the Feinberg-Horodecki equation, with the improved deformed exponential-type potential which is constructed by temporal counterpart of the spatial form of these potentials. We also plot the variations of the improved deformed exponential-type potential with its momentum eigenvalues for few quantized states against the screening parameter.展开更多
In this paper,the explicit estimates of central moments for one kind of exponential-type operators are derived.The estimates play an essential role in studying the explicit approximation properties of this family of o...In this paper,the explicit estimates of central moments for one kind of exponential-type operators are derived.The estimates play an essential role in studying the explicit approximation properties of this family of operators.Using the proposed method,the results of Ditzian and Totik in 1987,Guo and Qi in 2007,and Mahmudov in 2010 can be improved respectively.展开更多
Some exponential type representation formulas for C-semigroups are given in Banach space. Moreover, we obtain a corresponding Voronovskaja - type asymptotic formula.
We propose a six-parameter exponential-type potential (SPEP), which has been shown to be a shape-invariant potential with a translation of parameters. For this reducible potential, the exact energy levels are obtained...We propose a six-parameter exponential-type potential (SPEP), which has been shown to be a shape-invariant potential with a translation of parameters. For this reducible potential, the exact energy levels are obtained byusing the supersymmetric shape invariance technique. Choosing appropriate parameters, four classes of exponential-typepotentials and their exact energy spectra are reduced from the SPEP and a general energy level formula, respectively.Each class shows the identity except for the different definitions of parameters.展开更多
文摘The identity and the supersymmetry shape invariance for a class of exponential-type molecule potentials are studied by introducing a deformed five-parameter exponential-type potential (DFPEP) and via the multi-parameter deformations. It has been shown that the DFPEP is a shape-invariant potential with a translation of parameters. By making use of the shape invariance approach, the exact energy levels are determined for the bound states with zero angular momentum. A class of molecule potentials and their exact energy spectra for the zero angular momentum states are reduced from the DFPEP and a general energy spectrum formula, respectively. The interrelations for some molecule potentials are also discussed.
基金Supported by the National Natural Science Foundation of China under Grant No.10675097the Sichuan Province Foundation of China for Fundamental Research Projects under Grant No.2018JY0468
文摘The dissociation energy and equilibrium bond length as explicit parameters are used to establish an improved five-parameter exponential-type potential energy model for diatomic molecules. We demonstrate that the five-parameter exponential-type potential is identical to the Tietz potential for diatomic molecules. It is observed that the improved five-parameter exponential-type potential can well model the internuclear interaction potential energy curve for the ground electronic state of the carbon monoxide molecule by the utilization of the experimental values of three molecular constants.
文摘We obtain the quantized momentum eigenvalues, <em>P<sub>n</sub></em>, and the momentum eigenstates for the space-like Schrodinger equation, the Feinberg-Horodecki equation, with the improved deformed exponential-type potential which is constructed by temporal counterpart of the spatial form of these potentials. We also plot the variations of the improved deformed exponential-type potential with its momentum eigenvalues for few quantized states against the screening parameter.
基金Supported by National Natural Science Foundation of China(No.60872161,No.10971251)
文摘In this paper,the explicit estimates of central moments for one kind of exponential-type operators are derived.The estimates play an essential role in studying the explicit approximation properties of this family of operators.Using the proposed method,the results of Ditzian and Totik in 1987,Guo and Qi in 2007,and Mahmudov in 2010 can be improved respectively.
文摘Some exponential type representation formulas for C-semigroups are given in Banach space. Moreover, we obtain a corresponding Voronovskaja - type asymptotic formula.
文摘We propose a six-parameter exponential-type potential (SPEP), which has been shown to be a shape-invariant potential with a translation of parameters. For this reducible potential, the exact energy levels are obtained byusing the supersymmetric shape invariance technique. Choosing appropriate parameters, four classes of exponential-typepotentials and their exact energy spectra are reduced from the SPEP and a general energy level formula, respectively.Each class shows the identity except for the different definitions of parameters.
