def test_commutation():
n, m = symbols("n,m", above_fermi=True)
c = Commutator(B(0), Bd(0))
assert c == 1
c = Commutator(Bd(0), B(0))
assert c == -1
c = Commutator(B(n), Bd(0))
assert c == KroneckerDelta(n, 0)
c = Commutator(B(0), Bd(0))
e = simplify(apply_operators(c * BKet([n])))
assert e == BKet([n])
c = Commutator(B(0), B(1))
e = simplify(apply_operators(c * BKet([n, m])))
assert e == 0
c = Commutator(F(m), Fd(m))
assert c == +1 - 2 * NO(Fd(m) * F(m))
c = Commutator(Fd(m), F(m))
assert c.expand() == -1 + 2 * NO(Fd(m) * F(m))
C = Commutator
X, Y, Z = symbols('X,Y,Z', commutative=False)
assert C(C(X, Y), Z) != 0
assert C(C(X, Z), Y) != 0
assert C(Y, C(X, Z)) != 0
i, j, k, l = symbols('i,j,k,l', below_fermi=True)
a, b, c, d = symbols('a,b,c,d', above_fermi=True)
p, q, r, s = symbols('p,q,r,s')
D = KroneckerDelta
assert C(Fd(a), F(i)) == -2 * NO(F(i) * Fd(a))
assert C(Fd(j), NO(Fd(a) * F(i))).doit(wicks=True) == -D(j, i) * Fd(a)
assert C(Fd(a) * F(i), Fd(b) * F(j)).doit(wicks=True) == 0
def test_commutation():
c = commutator(B(0), Bd(0))
e = simplify(apply_operators(c*Ket([n])))
assert e == Ket([n])
c = commutator(B(0), B(1))
e = simplify(apply_operators(c*Ket([n,m])))
assert e == 0
def test_commutation():
c = commutator(B(0), Bd(0))
e = simplify(apply_operators(c * Ket([n])))
assert e == Ket([n])
c = commutator(B(0), B(1))
e = simplify(apply_operators(c * Ket([n, m])))
assert e == 0
def test_commutation():
n, m = symbols("n,m", above_fermi=True)
c = Commutator(B(0), Bd(0))
assert c == 1
c = Commutator(Bd(0), B(0))
assert c == -1
c = Commutator(B(n), Bd(0))
assert c == KroneckerDelta(n, 0)
c = Commutator(B(0), Bd(0))
e = simplify(apply_operators(c*BKet([n])))
assert e == BKet([n])
c = Commutator(B(0), B(1))
e = simplify(apply_operators(c*BKet([n, m])))
assert e == 0
c = Commutator(F(m), Fd(m))
assert c == +1 - 2*NO(Fd(m)*F(m))
c = Commutator(Fd(m), F(m))
assert c == -1 + 2*NO(Fd(m)*F(m))
C = Commutator
X, Y, Z = symbols('X,Y,Z', commutative=False)
assert C(C(X, Y), Z) != 0
assert C(C(X, Z), Y) != 0
assert C(Y, C(X, Z)) != 0
i, j, k, l = symbols('i,j,k,l', below_fermi=True)
a, b, c, d = symbols('a,b,c,d', above_fermi=True)
p, q, r, s = symbols('p,q,r,s')
D = KroneckerDelta
assert C(Fd(a), F(i)) == -2*NO(F(i)*Fd(a))
assert C(Fd(j), NO(Fd(a)*F(i))).doit(wicks=True) == -D(j, i)*Fd(a)
assert C(Fd(a)*F(i), Fd(b)*F(j)).doit(wicks=True) == 0
def test_commutation():
n, m = symbols("n,m", above_fermi=True)
c = Commutator(B(0), Bd(0))
assert c == 1
c = Commutator(Bd(0), B(0))
assert c == -1
c = Commutator(B(n), Bd(0))
assert c == KroneckerDelta(n, 0)
c = Commutator(B(0), B(0))
assert c == 0
c = Commutator(B(0), Bd(0))
e = simplify(apply_operators(c * BKet([n])))
assert e == BKet([n])
c = Commutator(B(0), B(1))
e = simplify(apply_operators(c * BKet([n, m])))
assert e == 0
c = Commutator(F(m), Fd(m))
assert c == +1 - 2 * NO(Fd(m) * F(m))
c = Commutator(Fd(m), F(m))
assert c.expand() == -1 + 2 * NO(Fd(m) * F(m))
C = Commutator
X, Y, Z = symbols("X,Y,Z", commutative=False)
assert C(C(X, Y), Z) != 0
assert C(C(X, Z), Y) != 0
assert C(Y, C(X, Z)) != 0
i, j, k, l = symbols("i,j,k,l", below_fermi=True)
a, b, c, d = symbols("a,b,c,d", above_fermi=True)
p, q, r, s = symbols("p,q,r,s")
D = KroneckerDelta
assert C(Fd(a), F(i)) == -2 * NO(F(i) * Fd(a))
assert C(Fd(j), NO(Fd(a) * F(i))).doit(wicks=True) == -D(j, i) * Fd(a)
assert C(Fd(a) * F(i), Fd(b) * F(j)).doit(wicks=True) == 0
c1 = Commutator(F(a), Fd(a))
assert Commutator.eval(c1, c1) == 0
c = Commutator(Fd(a) * F(i), Fd(b) * F(j))
assert latex(c) == r"\left[a^\dagger_{a} a_{i},a^\dagger_{b} a_{j}\right]"
assert (
repr(c)
== "Commutator(CreateFermion(a)*AnnihilateFermion(i),CreateFermion(b)*AnnihilateFermion(j))"
)
assert (
str(c)
== "[CreateFermion(a)*AnnihilateFermion(i),CreateFermion(b)*AnnihilateFermion(j)]"
)
def test_symbolic_matrix_elements():
n, m = symbols('n m')
s1 = BBra([n])
s2 = BKet([m])
o = B(0)
e = apply_operators(s1*o*s2)
assert e == sqrt(m)*KroneckerDelta(n, m-1)
def test_symbolic_matrix_elements():
n, m = symbols("n,m")
s1 = BBra([n])
s2 = BKet([m])
o = B(0)
e = apply_operators(s1 * o * s2)
assert e == sqrt(m) * KroneckerDelta(n, m - 1)
def test_commutation():
n, m = symbols("n,m", above_fermi=True)
c = Commutator(B(0), Bd(0))
assert c == 1
c = Commutator(Bd(0), B(0))
assert c == -1
c = Commutator(B(n), Bd(0))
assert c == KroneckerDelta(n, 0)
c = Commutator(B(0), B(0))
assert c == 0
c = Commutator(B(0), Bd(0))
e = simplify(apply_operators(c*BKet([n])))
assert e == BKet([n])
c = Commutator(B(0), B(1))
e = simplify(apply_operators(c*BKet([n, m])))
assert e == 0
c = Commutator(F(m), Fd(m))
assert c == +1 - 2*NO(Fd(m)*F(m))
c = Commutator(Fd(m), F(m))
assert c.expand() == -1 + 2*NO(Fd(m)*F(m))
C = Commutator
X, Y, Z = symbols('X,Y,Z', commutative=False)
assert C(C(X, Y), Z) != 0
assert C(C(X, Z), Y) != 0
assert C(Y, C(X, Z)) != 0
i, j, k, l = symbols('i,j,k,l', below_fermi=True)
a, b, c, d = symbols('a,b,c,d', above_fermi=True)
p, q, r, s = symbols('p,q,r,s')
D = KroneckerDelta
assert C(Fd(a), F(i)) == -2*NO(F(i)*Fd(a))
assert C(Fd(j), NO(Fd(a)*F(i))).doit(wicks=True) == -D(j, i)*Fd(a)
assert C(Fd(a)*F(i), Fd(b)*F(j)).doit(wicks=True) == 0
c1 = Commutator(F(a), Fd(a))
assert Commutator.eval(c1, c1) == 0
c = Commutator(Fd(a)*F(i),Fd(b)*F(j))
assert latex(c) == r'\left[a^\dagger_{a} a_{i},a^\dagger_{b} a_{j}\right]'
assert repr(c) == 'Commutator(CreateFermion(a)*AnnihilateFermion(i),CreateFermion(b)*AnnihilateFermion(j))'
assert str(c) == '[CreateFermion(a)*AnnihilateFermion(i),CreateFermion(b)*AnnihilateFermion(j)]'
def test_complex_apply():
n, m = symbols("n m")
o = Bd(0)*B(0)*Bd(1)*B(0)
e = apply_operators(o*BKet([n,m]))
answer = sqrt(n)*sqrt(m+1)*(-1+n)*BKet([-1+n,1+m])
assert expand(e) == expand(answer)
def test_number_operator():
n = symbols("n")
o = Bd(0) * B(0)
e = apply_operators(o * BKet([n]))
assert e == n * BKet([n])
def test_number_operator():
o = Bd(0) * B(0)
e = apply_operators(o * Ket([n]))
assert e == n * Ket([n])
def test_basic_apply():
n = symbols("n")
e = B(0) * BKet([n])
assert apply_operators(e) == sqrt(n) * BKet([n - 1])
e = Bd(0) * BKet([n])
assert apply_operators(e) == sqrt(n + 1) * BKet([n + 1])
def test_complex_apply():
n, m = symbols("n,m")
o = Bd(0) * B(0) * Bd(1) * B(0)
e = apply_operators(o * BKet([n, m]))
answer = sqrt(n) * sqrt(m + 1) * (-1 + n) * BKet([-1 + n, 1 + m])
assert expand(e) == expand(answer)
def test_number_operator():
o = Bd(0)*B(0)
e = apply_operators(o*Ket([n]))
assert e == n*Ket([n])
def test_basic_apply():
e = B(0)*Ket([n])
assert apply_operators(e) == sqrt(n)*Ket([n-1])
e = Bd(0)*Ket([n])
assert apply_operators(e) == sqrt(n+1)*Ket([n+1])
def test_number_operator():
n = symbols("n")
o = Bd(0)*B(0)
e = apply_operators(o*BKet([n]))
assert e == n*BKet([n])
def test_basic_apply():
e = B(0) * Ket([n])
assert apply_operators(e) == sqrt(n) * Ket([n - 1])
e = Bd(0) * Ket([n])
assert apply_operators(e) == sqrt(n + 1) * Ket([n + 1])
def test_basic_apply():
n = symbols("n")
e = B(0)*BKet([n])
assert apply_operators(e) == sqrt(n)*BKet([n-1])
e = Bd(0)*BKet([n])
assert apply_operators(e) == sqrt(n+1)*BKet([n+1])
