def test_Pauli():
sigma1 = Pauli(1)
sigma2 = Pauli(2)
sigma3 = Pauli(3)
assert sigma1 == sigma1
assert sigma1 != sigma2
assert sigma1 * sigma2 == I * sigma3
assert sigma3 * sigma1 == I * sigma2
assert sigma2 * sigma3 == I * sigma1
assert sigma1 * sigma1 == 1
assert sigma2 * sigma2 == 1
assert sigma3 * sigma3 == 1
assert sigma1**0 == 1
assert sigma1**1 == sigma1
assert sigma1**2 == 1
assert sigma1**3 == sigma1
assert sigma1**4 == 1
assert sigma3**2 == 1
assert sigma1 * 2 * sigma1 == 2
def symbolic_pauli_product(*args, as_tensor_product=False):
"""
Return symbolic sympy object represing product of Pauli matrices.
"""
if as_tensor_product:
tensor_product_elems = []
for arg in args:
if arg == 0:
tensor_product_elems.append(1)
else:
tensor_product_elems.append(Pauli(arg))
return TensorProduct(*tensor_product_elems)
out_expr = sympy.Integer(1)
for pos, arg in enumerate(args):
if arg != 0:
out_expr *= sympy.Symbol(['X', 'Y', 'Z'][arg - 1] + '_' +
str(pos + 1),
commutative=False)
return out_expr
from sympy import I, symbols
from sympy.physics.paulialgebra import Pauli
from sympy.testing.pytest import XFAIL
from sympy.physics.quantum import TensorProduct
sigma1 = Pauli(1)
sigma2 = Pauli(2)
sigma3 = Pauli(3)
tau1 = symbols("tau1", commutative=False)
def test_Pauli():
assert sigma1 == sigma1
assert sigma1 != sigma2
assert sigma1 * sigma2 == I * sigma3
assert sigma3 * sigma1 == I * sigma2
assert sigma2 * sigma3 == I * sigma1
assert sigma1 * sigma1 == 1
assert sigma2 * sigma2 == 1
assert sigma3 * sigma3 == 1
assert sigma1**0 == 1
assert sigma1**1 == sigma1
assert sigma1**2 == 1
assert sigma1**3 == sigma1
assert sigma1**4 == 1
def test_physics():
for c in (Unit, meter, Pauli, Pauli(1)):
check(c)
def test_sympy__physics__paulialgebra__Pauli():
from sympy.physics.paulialgebra import Pauli
assert _test_args(Pauli(1))
def test_physics():
for c in (Unit, Unit("meter", "m"), Pauli, Pauli(1)):
check(c)
from sympy.physics.paulialgebra import Pauli, evaluate_pauli_product
from sympy.physics.matrices import mdft, mgamma, msigma, pat_matrix
mdft(4) # expression of discrete Fourier transform as a matrix multiplication
mgamma(2) # Dirac gamma matrix in the Dirac representation
msigma(2) # Pauli matrix with (1,2,3)
pat_matrix(
3, 1, 0, 0
) # computer Parallel Axis Theorem matrix to translate the inertia matrix a distance of dx, dy, dz for a body of mass m.
evaluate_pauli_product(4 * x * Pauli(3) * Pauli(2))
from sympy.physics.paulialgebra import Pauli import sympy as sym import numpy as np #np.array(Pauli(1)).astype(np.complex) p1 = sym.N(Pauli(1)) print(p1)