受微扰的二维各向同性谐振子系统的守恒量
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摘要
采用扩展的P-S方法.首先,假定受微扰的二维各向同性谐振子系统存在守恒量;其次,分别用未知函数R,S去乘以恒为零的1-形式的微分式;然后,通过比较各系数求得未知函数R和S.由此求得了受微扰的二维各向同性谐振子系统的两守恒量I1和I2.研究并讨论了微扰系统守恒量的物理意义.结果表明,二维各向同性谐振子在受到微扰后,由于对称性的降低,其守恒量也发生了变化,在Lagrange体系中,其对称性与守恒量的关系可由Noether定理给出.
Extended Prelle-Singer method is used. This paper is based on the assumption that there are conserved quantities in two-dimensional harmonic oscillator system by perturbation,uses unknown functions R,S respectively to multiply a constant to zero 1-form style differential,and calculates coefficient R and S by comparing the integral multiplier. This paper discusses the physical significance of two conserved quantities. The results showed two-dimensional harmonic oscillator system by perturbation. Due to lower symmetry,the conserved quantity changed. In the Lagrange system,the relationship between symmetry and conserved quantities is given by Noether theorem.
Extended Prelle-Singer method is used. This paper is based on the assumption that there are conserved quantities in two-dimensional harmonic oscillator system by perturbation,uses unknown functions R,S respectively to multiply a constant to zero 1-form style differential,and calculates coefficient R and S by comparing the integral multiplier. This paper discusses the physical significance of two conserved quantities. The results showed two-dimensional harmonic oscillator system by perturbation. Due to lower symmetry,the conserved quantity changed. In the Lagrange system,the relationship between symmetry and conserved quantities is given by Noether theorem.
引文
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[15]梅凤翔.李群和李代数对约束力学系统的应用[M].北京:科学出版社,1999:260-262.
[2]张永德.量子力学[M].北京:科学出版社,2005:425-427.
[3]钱伯初,曾谨言.量子力学习题精选与剖析[M].上册.北京:科学出版社,1999:85-87.
[4]王竹溪,郭敦仁.特殊函数概论[M].北京:科学出版社,1979:364.
[5]张永德.力学[M].下册.北京:科学出版社,2005:635-638.
[6]赵素琴.均匀电场、磁场中三维各向同性谐振子的壳结构[J].西南民族大学学报,2006,32(5):1020-1024.
[7]赵素琴.均匀磁场中三维各向同性谐振子微扰矩阵元的普遍表达式[J].大学物理,2007,26(2):5-7.
[8]楼智美.二阶非线性耦合动力学系统守恒量的扩展Prelle-Singer求法与对称性研究[J].物理学报,2010,59(02):719-723.
[9]赵跃宇,梅凤翔.力学系统的对称性与不变量[M].北京:科学出版社,1999:25-30.
[10]楼智美,梅凤翔,陈子栋.弱非线性耦合二维各向异性谐振子的一阶近似Lie对称性与近似守恒量[J].物理学报,2012,61(11):204-209.
[11]楼智美.哈密顿Erm akov系统的形式不变性[J].物理学报,2005,54(5):1969-1971.
[12]楼智美.一类多自由度线性耦合系统的对称性与守恒量研究[J].物理学报,2007,56(5):2475-2478.
[13]楼智美.非中心力场中经典粒子的轨道参数方程与对称性[J].物理学报,2005,54(4):1460-1463.
[14]梅凤翔.动力学逆问题[M].北京:国防工业出版社,2009:51-61.
[15]梅凤翔.李群和李代数对约束力学系统的应用[M].北京:科学出版社,1999:260-262.