克莱布希-戈尔丹系数

克莱布希-戈登系数。

class sympy.physics.quantum.cg.CG(j1, m1, j2, m2, j3, m3)

Class for Clebsch-Gordan coefficient.

参数:

j1, m1, j2, m2 : Number, Symbol

Angular momenta of states 1 and 2.

j3, m3: Number, Symbol

Total angular momentum of the coupled system.

解释

Clebsch-Gordan coefficients describe the angular momentum coupling between two systems. The coefficients give the expansion of a coupled total angular momentum state and an uncoupled tensor product state. The Clebsch-Gordan coefficients are defined as [R750]:

\[C^{j_3,m_3}_{j_1,m_1,j_2,m_2} = \left\langle j_1,m_1;j_2,m_2 | j_3,m_3\right\rangle\]

实例

定义Clebsch-Gordan系数并计算其值

>>> from sympy.physics.quantum.cg import CG
>>> from sympy import S
>>> cg = CG(S(3)/2, S(3)/2, S(1)/2, -S(1)/2, 1, 1)
>>> cg
CG(3/2, 3/2, 1/2, -1/2, 1, 1)
>>> cg.doit()
sqrt(3)/2
>>> CG(j1=S(1)/2, m1=-S(1)/2, j2=S(1)/2, m2=+S(1)/2, j3=1, m3=0).doit()
sqrt(2)/2

Compare [R751].

参见

Wigner3j

Wigner-3j符号

工具书类

[R750] (1,2)

Varshalovich，D A，角动量的量子理论。1988

[R751] (1,2)

Clebsch-Gordan Coefficients, Spherical Harmonics, and d Functions in P.A. Zyla et al. (Particle Data Group), Prog. Theor. Exp. Phys. 2020, 083C01 (2020).

class sympy.physics.quantum.cg.Wigner3j(j1, m1, j2, m2, j3, m3)

Class for the Wigner-3j symbols.

参数:

j1、m1、j2、m2、j3、m3 ：数字，符号

确定耦合角动量系统角动量的术语。

解释

Wigner 3j-symbols are coefficients determined by the coupling of two angular momenta. When created, they are expressed as symbolic quantities that, for numerical parameters, can be evaluated using the .doit() method [R752].

实例

声明Wigner-3j系数并计算其值

>>> from sympy.physics.quantum.cg import Wigner3j
>>> w3j = Wigner3j(6,0,4,0,2,0)
>>> w3j
Wigner3j(6, 0, 4, 0, 2, 0)
>>> w3j.doit()
sqrt(715)/143

参见

CG

克莱布希-戈尔丹系数

工具书类

[R752] (1,2)

Varshalovich，D A，角动量的量子理论。1988

class sympy.physics.quantum.cg.Wigner6j(j1, j2, j12, j3, j, j23)

Wigner-6j符号类

参见

Wigner3j

Wigner-3j符号

class sympy.physics.quantum.cg.Wigner9j(j1, j2, j12, j3, j4, j34, j13, j24, j)

Wigner-9j符号类

参见

Wigner3j

Wigner-3j符号

sympy.physics.quantum.cg.cg_simp(e)

Simplify and combine CG coefficients.

解释

This function uses various symmetry and properties of sums and products of Clebsch-Gordan coefficients to simplify statements involving these terms [R753].

实例

将所有α的和简化为2*a+1

>>> from sympy.physics.quantum.cg import CG, cg_simp
>>> a = CG(1,1,0,0,1,1)
>>> b = CG(1,0,0,0,1,0)
>>> c = CG(1,-1,0,0,1,-1)
>>> cg_simp(a+b+c)
3

参见

CG

克莱布什-戈尔丹系数

工具书类

[R753] (1,2)

Varshalovich，D A，角动量的量子理论。1988