Based on the 3D electron's radial wave function of Co 2+ free ion,a Nephelauxetic effect modifying factor to modify the radial wave function is introduced when Co 2+ cations are put into the crystal fie...Based on the 3D electron's radial wave function of Co 2+ free ion,a Nephelauxetic effect modifying factor to modify the radial wave function is introduced when Co 2+ cations are put into the crystal field of Zn 1-x Co x Se.With the modified wave functions,the optical transitions for Zn 1-x Co x Se crystals are calculated.Moreover,based on the first principle of physics,the influences of high pressure to the Nephelauxetic effect modifying factor is considered,and the high pressure blue shift for the Zn 1-x Co x Se crystal absorption spectra are calculated and a shift rate of d E /d p =0 45meV/GPa is obtained.展开更多
The analytic solution of the radial Schrodinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely ana...The analytic solution of the radial Schrodinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely analytic solutions and the conditions that decide the existence of analytic solution have been searched when the potential of the radial Schrodinger equation is V（r） =α1r^8 ＋α2r^3 ＋ α3r^2 ＋β3r^-1 ＋β2r^-3 ＋β1r6-4. Generally speaking, there is only an approximate solution, but not analytic solution for SchrSdinger equation with several potentials＇ superposition. However, the conditions that decide the existence of analytic solution have been found and the analytic solution and its energy level structure are obtained for the Schrodinger equation with the potential which is motioned above in this paper. According to the single-value, finite and continuous standard of wave function in a quantum system, the authors firstly solve the asymptotic solution through the radial coordinate r → ∞ and r →0; secondly, they make the asymptotic solutions combining with the series solutions nearby the neighborhood of irregular singularities; and then they compare the power series coefficients, deduce a series of analytic solutions of the stationary state wave function and corresponding energy level structure by tight coupling among the coefficients of potential functions for the radial SchrSdinger equation; and lastly, they discuss the solutions and make conclusions.展开更多
文摘Based on the 3D electron's radial wave function of Co 2+ free ion,a Nephelauxetic effect modifying factor to modify the radial wave function is introduced when Co 2+ cations are put into the crystal field of Zn 1-x Co x Se.With the modified wave functions,the optical transitions for Zn 1-x Co x Se crystals are calculated.Moreover,based on the first principle of physics,the influences of high pressure to the Nephelauxetic effect modifying factor is considered,and the high pressure blue shift for the Zn 1-x Co x Se crystal absorption spectra are calculated and a shift rate of d E /d p =0 45meV/GPa is obtained.
基金supported by the National Natural Science Foundation of China under Grant No.10575140the Basic Research of Chongqing Education Committee under Grant No.KJ060813
文摘The analytic solution of the radial Schrodinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely analytic solutions and the conditions that decide the existence of analytic solution have been searched when the potential of the radial Schrodinger equation is V（r） =α1r^8 ＋α2r^3 ＋ α3r^2 ＋β3r^-1 ＋β2r^-3 ＋β1r6-4. Generally speaking, there is only an approximate solution, but not analytic solution for SchrSdinger equation with several potentials＇ superposition. However, the conditions that decide the existence of analytic solution have been found and the analytic solution and its energy level structure are obtained for the Schrodinger equation with the potential which is motioned above in this paper. According to the single-value, finite and continuous standard of wave function in a quantum system, the authors firstly solve the asymptotic solution through the radial coordinate r → ∞ and r →0; secondly, they make the asymptotic solutions combining with the series solutions nearby the neighborhood of irregular singularities; and then they compare the power series coefficients, deduce a series of analytic solutions of the stationary state wave function and corresponding energy level structure by tight coupling among the coefficients of potential functions for the radial SchrSdinger equation; and lastly, they discuss the solutions and make conclusions.
