Free longitudinal vibrations of non-uniform rods are investigated by a proposed method, which results in a series solution. In a special case, with the proposed method an exact solution with a concise form can be obta...Free longitudinal vibrations of non-uniform rods are investigated by a proposed method, which results in a series solution. In a special case, with the proposed method an exact solution with a concise form can be obtained, which imply four types of profiles with variation in geometry or material properties. However, the WKB (Wentzel-Kramers-Brillouin) method leads to a series solution, which is a Taylor expansion of the results of the proposed method. For the arbitrary non-uniform rods, the comparison indicates that the WKB method is simpler, but the convergent speed of the series solution resulting from the pro-posed method is faster than that of the WKB method, which is also validated numerically using an exact solution of a kind of non-uniform rods with Kummer functions.展开更多
采用6阶WKB方法,研究了带有整体单极子的Reissner-Nordstrm de Sitter黑洞时空中无质量狄拉克场扰动的似正规模。数值结果显示,该黑洞时空中无质量狄拉克场的似正规模频谱取决于黑洞的有效电荷Q和有效质量M、宇宙学常数Λ以及表征对...采用6阶WKB方法,研究了带有整体单极子的Reissner-Nordstrm de Sitter黑洞时空中无质量狄拉克场扰动的似正规模。数值结果显示,该黑洞时空中无质量狄拉克场的似正规模频谱取决于黑洞的有效电荷Q和有效质量M、宇宙学常数Λ以及表征对称性破缺的标度因子η。对于确定的|κ|、模数n、宇宙学常数Λ和b(和η有关),无质量狄拉克场的衰减在宇宙学常数Λ比较小时是随着Q的增加先变快后变慢,而当宇宙学常数比较大时,则是随着Q的增加而变快。对于确定的|κ|、n、Q和b,无质量狄拉克场的衰减随着Λ的增加而变慢。展开更多
By using the supersymmetric quantum mechanics and shape invariance concept, we study the Dirac equation with the hyperbolic Scarf potential and the exact energy spectrum is obtained. Also, we calculate the bound state...By using the supersymmetric quantum mechanics and shape invariance concept, we study the Dirac equation with the hyperbolic Scarf potential and the exact energy spectrum is obtained. Also, we calculate the bound state energy eigenvalues by using the supersymmetric WKB approximation approach so that we get the same results.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 11072157 and 10932006) the Program for Chang-jiang Scholars and Innovative Research Team in University (IRT0971).
文摘Free longitudinal vibrations of non-uniform rods are investigated by a proposed method, which results in a series solution. In a special case, with the proposed method an exact solution with a concise form can be obtained, which imply four types of profiles with variation in geometry or material properties. However, the WKB (Wentzel-Kramers-Brillouin) method leads to a series solution, which is a Taylor expansion of the results of the proposed method. For the arbitrary non-uniform rods, the comparison indicates that the WKB method is simpler, but the convergent speed of the series solution resulting from the pro-posed method is faster than that of the WKB method, which is also validated numerically using an exact solution of a kind of non-uniform rods with Kummer functions.
文摘采用6阶WKB方法,研究了带有整体单极子的Reissner-Nordstrm de Sitter黑洞时空中无质量狄拉克场扰动的似正规模。数值结果显示,该黑洞时空中无质量狄拉克场的似正规模频谱取决于黑洞的有效电荷Q和有效质量M、宇宙学常数Λ以及表征对称性破缺的标度因子η。对于确定的|κ|、模数n、宇宙学常数Λ和b(和η有关),无质量狄拉克场的衰减在宇宙学常数Λ比较小时是随着Q的增加先变快后变慢,而当宇宙学常数比较大时,则是随着Q的增加而变快。对于确定的|κ|、n、Q和b,无质量狄拉克场的衰减随着Λ的增加而变慢。
文摘By using the supersymmetric quantum mechanics and shape invariance concept, we study the Dirac equation with the hyperbolic Scarf potential and the exact energy spectrum is obtained. Also, we calculate the bound state energy eigenvalues by using the supersymmetric WKB approximation approach so that we get the same results.
