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
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