from __future__ import division
from sympy import cos, exp, expand, I, Matrix, pi, S, sin, sqrt, Sum, symbols
from sympy.abc import alpha, beta, gamma, j, m
from sympy.physics.quantum import hbar, represent, Commutator, InnerProduct
from sympy.physics.quantum.qapply import qapply
from sympy.physics.quantum.tensorproduct import TensorProduct
from sympy.physics.quantum.cg import CG
from sympy.physics.quantum.spin import (
Jx, Jy, Jz, Jplus, Jminus, J2,
JxBra, JyBra, JzBra,
JxKet, JyKet, JzKet,
JxKetCoupled, JyKetCoupled, JzKetCoupled,
couple, uncouple,
Rotation, WignerD
)
from sympy.utilities.pytest import raises
j1,j2,j3,j4,m1,m2,m3,m4 = symbols('j1:5 m1:5')
j12,j13,j24,j34,j123,j134,mi,mi1,mp = symbols('j12 j13 j24 j34 j123 j134 mi mi1 mp')
def test_represent_spin_operators():
assert represent(Jx) == hbar*Matrix([[0,1],[1,0]])/2
assert represent(Jx, j=1) == hbar*sqrt(2)*Matrix([[0,1,0],[1,0,1],[0,1,0]])/2
assert represent(Jy) == hbar*I*Matrix([[0,-1],[1,0]])/2
assert represent(Jy, j=1) == hbar*I*sqrt(2)*Matrix([[0,-1,0],[1,0,-1],[0,1,0]])/2
assert represent(Jz) == hbar*Matrix([[1,0],[0,-1]])/2
assert represent(Jz, j=1) == hbar*Matrix([[1,0,0],[0,0,0],[0,0,-1]])
def test_represent_spin_states():
# Jx basis
assert represent(JxKet(S(1)/2,S(1)/2), basis=Jx) == Matrix([1,0])
assert represent(JxKet(S(1)/2,-S(1)/2), basis=Jx) == Matrix([0,1])
assert represent(JxKet(1,1), basis=Jx) == Matrix([1,0,0])
assert represent(JxKet(1,0), basis=Jx) == Matrix([0,1,0])
assert represent(JxKet(1,-1), basis=Jx) == Matrix([0,0,1])
assert represent(JyKet(S(1)/2,S(1)/2), basis=Jx) == Matrix([exp(-I*pi/4),0])
assert represent(JyKet(S(1)/2,-S(1)/2), basis=Jx) == Matrix([0,exp(I*pi/4)])
assert represent(JyKet(1,1), basis=Jx) == Matrix([-I,0,0])
assert represent(JyKet(1,0), basis=Jx) == Matrix([0,1,0])
assert represent(JyKet(1,-1), basis=Jx) == Matrix([0,0,I])
assert represent(JzKet(S(1)/2,S(1)/2), basis=Jx) == sqrt(2)*Matrix([-1,1])/2
assert represent(JzKet(S(1)/2,-S(1)/2), basis=Jx) == sqrt(2)*Matrix([-1,-1])/2
assert represent(JzKet(1,1), basis=Jx) == Matrix([1,-sqrt(2),1])/2
assert represent(JzKet(1,0), basis=Jx) == sqrt(2)*Matrix([1,0,-1])/2
assert represent(JzKet(1,-1), basis=Jx) == Matrix([1,sqrt(2),1])/2
# Jy basis
assert represent(JxKet(S(1)/2,S(1)/2), basis=Jy) == Matrix([exp(-3*I*pi/4),0])
assert represent(JxKet(S(1)/2,-S(1)/2), basis=Jy) == Matrix([0,exp(3*I*pi/4)])
assert represent(JxKet(1,1), basis=Jy) == Matrix([I,0,0])
assert represent(JxKet(1,0), basis=Jy) == Matrix([0,1,0])
assert represent(JxKet(1,-1), basis=Jy) == Matrix([0,0,-I])
assert represent(JyKet(S(1)/2,S(1)/2), basis=Jy) == Matrix([1,0])
assert represent(JyKet(S(1)/2,-S(1)/2), basis=Jy) == Matrix([0,1])
assert represent(JyKet(1,1), basis=Jy) == Matrix([1,0,0])
assert represent(JyKet(1,0), basis=Jy) == Matrix([0,1,0])
assert represent(JyKet(1,-1), basis=Jy) == Matrix([0,0,1])
assert represent(JzKet(S(1)/2,S(1)/2), basis=Jy) == sqrt(2)*Matrix([-1,I])/2
assert represent(JzKet(S(1)/2,-S(1)/2), basis=Jy) == sqrt(2)*Matrix([I,-1])/2
assert represent(JzKet(1,1), basis=Jy) == Matrix([1,-I*sqrt(2),-1])/2
assert represent(JzKet(1,0), basis=Jy) == Matrix([-sqrt(2)*I,0,-sqrt(2)*I])/2
assert represent(JzKet(1,-1), basis=Jy) == Matrix([-1,-sqrt(2)*I,1])/2
# Jz basis
assert represent(JxKet(S(1)/2,S(1)/2), basis=Jz) == sqrt(2)*Matrix([1,1])/2
assert represent(JxKet(S(1)/2,-S(1)/2), basis=Jz) == sqrt(2)*Matrix([-1,1])/2
assert represent(JxKet(1,1), basis=Jz) == Matrix([1,sqrt(2),1])/2
assert represent(JxKet(1,0), basis=Jz) == sqrt(2)*Matrix([-1,0,1])/2
assert represent(JxKet(1,-1), basis=Jz) == Matrix([1,-sqrt(2),1])/2
assert represent(JyKet(S(1)/2,S(1)/2), basis=Jz) == sqrt(2)*Matrix([-1,-I])/2
assert represent(JyKet(S(1)/2,-S(1)/2), basis=Jz) == sqrt(2)*Matrix([-I,-1])/2
assert represent(JyKet(1,1), basis=Jz) == Matrix([1,sqrt(2)*I,-1])/2
assert represent(JyKet(1,0), basis=Jz) == sqrt(2)*Matrix([I,0,I])/2
assert represent(JyKet(1,-1), basis=Jz) == Matrix([-1,sqrt(2)*I,1])/2
assert represent(JzKet(S(1)/2,S(1)/2), basis=Jz) == Matrix([1,0])
assert represent(JzKet(S(1)/2,-S(1)/2), basis=Jz) == Matrix([0,1])
assert represent(JzKet(1,1), basis=Jz) == Matrix([1,0,0])
assert represent(JzKet(1,0), basis=Jz) == Matrix([0,1,0])
assert represent(JzKet(1,-1), basis=Jz) == Matrix([0,0,1])
def test_represent_uncoupled_states():
# Jx basis
assert represent(TensorProduct(JxKet(S(1)/2,S(1)/2),JxKet(S(1)/2,S(1)/2)), basis=Jx) == \
Matrix([1,0,0,0])
assert represent(TensorProduct(JxKet(S(1)/2,S(1)/2),JxKet(S(1)/2,-S(1)/2)), basis=Jx) == \
Matrix([0,1,0,0])
assert represent(TensorProduct(JxKet(S(1)/2,-S(1)/2),JxKet(S(1)/2,S(1)/2)), basis=Jx) == \
Matrix([0,0,1,0])
assert represent(TensorProduct(JxKet(S(1)/2,-S(1)/2),JxKet(S(1)/2,-S(1)/2)), basis=Jx) == \
Matrix([0,0,0,1])
assert represent(TensorProduct(JyKet(S(1)/2,S(1)/2),JyKet(S(1)/2,S(1)/2)), basis=Jx) == \
Matrix([-I,0,0,0])
assert represent(TensorProduct(JyKet(S(1)/2,S(1)/2),JyKet(S(1)/2,-S(1)/2)), basis=Jx) == \
Matrix([0,1,0,0])
assert represent(TensorProduct(JyKet(S(1)/2,-S(1)/2),JyKet(S(1)/2,S(1)/2)), basis=Jx) == \
Matrix([0,0,1,0])
assert represent(TensorProduct(JyKet(S(1)/2,-S(1)/2),JyKet(S(1)/2,-S(1)/2)), basis=Jx) == \
Matrix([0,0,0,I])
assert represent(TensorProduct(JzKet(S(1)/2,S(1)/2),JzKet(S(1)/2,S(1)/2)), basis=Jx) == \
Matrix([S(1)/2,-S(1)/2,-S(1)/2,S(1)/2])
assert represent(TensorProduct(JzKet(S(1)/2,S(1)/2),JzKet(S(1)/2,-S(1)/2)), basis=Jx) == \
Matrix([S(1)/2,S(1)/2,-S(1)/2,-S(1)/2])
assert represent(TensorProduct(JzKet(S(1)/2,-S(1)/2),JzKet(S(1)/2,S(1)/2)), basis=Jx) == \
Matrix([S(1)/2,-S(1)/2,S(1)/2,-S(1)/2])
assert represent(TensorProduct(JzKet(S(1)/2,-S(1)/2),JzKet(S(1)/2,-S(1)/2)), basis=Jx) == \
Matrix([S(1)/2,S(1)/2,S(1)/2,S(1)/2])
# Jy basis
assert represent(TensorProduct(JxKet(S(1)/2,S(1)/2),JxKet(S(1)/2,S(1)/2)), basis=Jy) == \
Matrix([I,0,0,0])
assert represent(TensorProduct(JxKet(S(1)/2,S(1)/2),JxKet(S(1)/2,-S(1)/2)), basis=Jy) == \
Matrix([0,1,0,0])
assert represent(TensorProduct(JxKet(S(1)/2,-S(1)/2),JxKet(S(1)/2,S(1)/2)), basis=Jy) == \
Matrix([0,0,1,0])
assert represent(TensorProduct(JxKet(S(1)/2,-S(1)/2),JxKet(S(1)/2,-S(1)/2)), basis=Jy) == \
Matrix([0,0,0,-I])
assert represent(TensorProduct(JyKet(S(1)/2,S(1)/2),JyKet(S(1)/2,S(1)/2)), basis=Jy) == \
Matrix([1,0,0,0])
assert represent(TensorProduct(JyKet(S(1)/2,S(1)/2),JyKet(S(1)/2,-S(1)/2)), basis=Jy) == \
Matrix([0,1,0,0])
assert represent(TensorProduct(JyKet(S(1)/2,-S(1)/2),JyKet(S(1)/2,S(1)/2)), basis=Jy) == \
Matrix([0,0,1,0])
assert represent(TensorProduct(JyKet(S(1)/2,-S(1)/2),JyKet(S(1)/2,-S(1)/2)), basis=Jy) == \
Matrix([0,0,0,1])
assert represent(TensorProduct(JzKet(S(1)/2,S(1)/2),JzKet(S(1)/2,S(1)/2)), basis=Jy) == \
Matrix([S(1)/2,-I/2,-I/2,-S(1)/2])
assert represent(TensorProduct(JzKet(S(1)/2,S(1)/2),JzKet(S(1)/2,-S(1)/2)), basis=Jy) == \
Matrix([-I/2,S(1)/2,-S(1)/2,-I/2])
assert represent(TensorProduct(JzKet(S(1)/2,-S(1)/2),JzKet(S(1)/2,S(1)/2)), basis=Jy) == \
Matrix([-I/2,-S(1)/2,S(1)/2,-I/2])
assert represent(TensorProduct(JzKet(S(1)/2,-S(1)/2),JzKet(S(1)/2,-S(1)/2)), basis=Jy) == \
Matrix([-S(1)/2,-I/2,-I/2,S(1)/2])
# Jz basis
assert represent(TensorProduct(JxKet(S(1)/2,S(1)/2),JxKet(S(1)/2,S(1)/2)), basis=Jz) == \
Matrix([S(1)/2,S(1)/2,S(1)/2,S(1)/2])
assert represent(TensorProduct(JxKet(S(1)/2,S(1)/2),JxKet(S(1)/2,-S(1)/2)), basis=Jz) == \
Matrix([-S(1)/2,S(1)/2,-S(1)/2,S(1)/2])
assert represent(TensorProduct(JxKe
sympy-0.7.2.tar.gz （1134个子文件） 
isympy.1 6KB AUTHORS 8KB apidoc.conf 233B multable.dat 2KB .DS_Store 12KB .DS_Store 6KB .DS_Store 6KB SymPy-Favicon.ico 6KB SymPy-Favicon-WithoutTail.ico 5KB ipythonrc-sympy 1KB isympy 11KB LICENSE 1KB LICENSE 1KB Makefile 5KB tutorial.mo 27KB tutorial.mo 23KB tutorial.mo 21KB tutorial.mo 18KB tutorial.mo 17KB tutorial.mo 15KB tutorial.mo 15KB
kin_1pt.pdf 13KB vec_dot.pdf 10KB simp_rot.pdf 9KB vec_simp_der.pdf 9KB kin_rolling.pdf 9KB kin_2pt.pdf 9KB kin_angvel2.pdf 8KB kin_angvel1.pdf 8KB vec_cross.pdf 7KB kin_2.pdf 7KB kin_angvel3.pdf 7KB kin_4.pdf 6KB vec_fix_notfix.pdf 6KB vec_rep.pdf 6KB ex_rd.pdf 6KB kin_1.pdf 6KB kin_3.pdf 6KB vec_add.pdf 5KB vec_mul.pdf 5KB PKG-INFO 1KB
SymPy-500x500-Logo-No-Transparency.png 172KB SymPy-500x500-Logo.png 172KB SymPy-500x500-Logo -No-Text.png 163KB SymPy-500x500-Logo-No-Transparency-No-Text.png 149KB SymPy-Logo-NoTail.png 146KB SymPy-NoTail-NoText.png 137KB winpdb2.png 92KB kleinj.png 76KB bi_c.png 66KB winpdb1.png 65KB ai_c.png 61KB kleinj2.png 60KB gi_c.png 56KB spherharm42.png 50KB spherharm43.png 47KB hi_c.png 46KB coulombg_c.png 45KB cplot.png 42KB spherharm44.png 40KB bessely_c.png 40KB coulombf_c.png 39KB spherharm41.png 37KB besselj_c.png 37KB hankel1_c.png 35KB hankel2_c.png 35KB besseli_c.png 34KB coulombf.png 34KB coulombg.png 33KB chebyt.png 32KB besselk_c.png 30KB lambertw_c.png 28KB pcfd.png 28KB legendre.png 27KB hankel2.png 26KB hankel1.png 26KB lommels1.png 26KB ai.png 26KB hermite.png 25KB bi.png 25KB ellipe.png 24KB splot.png 23KB spherharm40.png 23KB besselj.png 23KB chebyu.png 22KB ellipf.png 22KB ellippi.png 21KB plot.png 20KB sympylogo.png 19KB bessely.png 19KB ber.png 19KB laguerre.png 19KB besseli.png 19KB gi.png 18KB lommels2.png 17KB lambertw.png 15KB besselk.png 15KB ker.png 14KB ellipk.png 12KB hi.png 10KB共 1134 条
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