def test_create_f():
i, j, n, m = symbols("i,j,n,m")
o = Fd(i)
assert isinstance(o, CreateFermion)
o = o.subs(i, j)
assert o.atoms(Symbol) == {j}
o = Fd(1)
assert o.apply_operator(FKet([n])) == FKet([1, n])
assert o.apply_operator(FKet([n])) == -FKet([n, 1])
o = Fd(n)
assert o.apply_operator(FKet([])) == FKet([n])
vacuum = FKet([], fermi_level=4)
assert vacuum == FKet([], fermi_level=4)
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")
assert Fd(i).apply_operator(FKet([i, j, k], 4)) == FKet([j, k], 4)
assert Fd(a).apply_operator(FKet([i, b, k], 4)) == FKet([a, i, b, k], 4)
assert Dagger(B(p)).apply_operator(q) == q * CreateBoson(p)
assert repr(Fd(p)) == "CreateFermion(p)"
assert srepr(Fd(p)) == "CreateFermion(Symbol('p'))"
assert latex(Fd(p)) == r"a^\dagger_{p}"
def test_inner_product():
i, j, k, l = symbols("i,j,k,l")
s1 = BBra([0])
s2 = BKet([1])
assert InnerProduct(s1, Dagger(s1)) == 1
assert InnerProduct(s1, s2) == 0
s1 = BBra([i, j])
s2 = BKet([k, l])
r = InnerProduct(s1, s2)
assert r == KroneckerDelta(i, k) * KroneckerDelta(j, l)
def test_inner_product():
i, j, k, l = var('i j k l')
s1 = Bra([0])
s2 = Ket([1])
assert InnerProduct(s1, Dagger(s1)) == 1
assert InnerProduct(s1, s2) == 0
s1 = Bra([i, j])
s2 = Ket([k, l])
r = InnerProduct(s1, s2)
assert r == KroneckerDelta(i, k) * KroneckerDelta(j, l)
def test_dagger():
i, j, n, m = symbols("i,j,n,m")
assert Dagger(1) == 1
assert Dagger(1.0) == 1.0
assert Dagger(2 * I) == -2 * I
assert Dagger(S.Half * I / 3.0) == I * Rational(-1, 2) / 3.0
assert Dagger(BKet([n])) == BBra([n])
assert Dagger(B(0)) == Bd(0)
assert Dagger(Bd(0)) == B(0)
assert Dagger(B(n)) == Bd(n)
assert Dagger(Bd(n)) == B(n)
assert Dagger(B(0) + B(1)) == Bd(0) + Bd(1)
assert Dagger(n * m) == Dagger(n) * Dagger(m) # n, m commute
assert Dagger(B(n) * B(m)) == Bd(m) * Bd(n)
assert Dagger(B(n) ** 10) == Dagger(B(n)) ** 10
assert Dagger("a") == Dagger(Symbol("a"))
assert Dagger(Dagger("a")) == Symbol("a")
def test_dagger():
i, j, n, m = symbols('i,j,n,m')
assert Dagger(1) == 1
assert Dagger(1.0) == 1.0
assert Dagger(2*I) == -2*I
assert Dagger(Rational(1, 2)*I/3.0) == -Rational(1, 2)*I/3.0
assert Dagger(BKet([n])) == BBra([n])
assert Dagger(B(0)) == Bd(0)
assert Dagger(Bd(0)) == B(0)
assert Dagger(B(n)) == Bd(n)
assert Dagger(Bd(n)) == B(n)
assert Dagger(B(0) + B(1)) == Bd(0) + Bd(1)
assert Dagger(n*m) == Dagger(n)*Dagger(m) # n, m commute
assert Dagger(B(n)*B(m)) == Bd(m)*Bd(n)
assert Dagger(B(n)**10) == Dagger(B(n))**10
assert Dagger('a') == Dagger(Symbol('a'))
assert Dagger(Dagger('a')) == Symbol('a')
def test_dagger():
i, j, n, m = var('i j n m')
assert Dagger(1) == 1
assert Dagger(1.0) == 1.0
assert Dagger(2 * I) == -2 * I
assert Dagger(Rational(1, 2) * I / 3.0) == -Rational(1, 2) * I / 3.0
assert Dagger(Ket([n])) == Bra([n])
assert Dagger(B(0)) == Bd(0)
assert Dagger(Bd(0)) == B(0)
assert Dagger(B(n)) == Bd(n)
assert Dagger(Bd(n)) == B(n)
assert Dagger(B(0) + B(1)) == Bd(0) + Bd(1)
assert Dagger(n * m) == Dagger(n) * Dagger(m) # n, m commute
assert Dagger(B(n) * B(m)) == Bd(m) * Bd(n)
assert Dagger(B(n)**10) == Dagger(B(n))**10
