def test_p():
assert Px.hilbert_space == L2(Interval(S.NegativeInfinity, S.Infinity))
assert apply_operators(Px*PxKet(px)) == px*PxKet(px)
assert PxKet(px).dual_class == PxBra
assert PxBra(x).dual_class == PxKet
assert (Dagger(PxKet(py))*PxKet(px)).doit() == DiracDelta(px-py)
assert (XBra(x)*PxKet(px)).doit() ==\
exp(I*x*px/hbar)/sqrt(2*pi*hbar)
assert represent(PxKet(px)) == px
def test_x():
assert X.hilbert_space == L2(Interval(S.NegativeInfinity, S.Infinity))
assert Commutator(X, Px).doit() == I*hbar
assert apply_operators(X*XKet(x)) == x*XKet(x)
assert XKet(x).dual_class == XBra
assert XBra(x).dual_class == XKet
assert (Dagger(XKet(y))*XKet(x)).doit() == DiracDelta(x-y)
assert (PxBra(px)*XKet(x)).doit() ==\
exp(-I*x*px/hbar)/sqrt(2*pi*hbar)
assert represent(XKet(x)) == x
assert XBra(x).position == x
def test_H():
assert PIABHamiltonian('H').hilbert_space ==\
L2(Interval(S.NegativeInfinity,S.Infinity))
assert apply_operators(PIABHamiltonian('H')*PIABKet(n)) ==\
(n**2*pi**2*hbar**2)/(2*m*L**2)*PIABKet(n)
def test_jplus():
assert Commutator(Jplus, Jminus).doit() == 2*hbar*Jz
assert apply_operators(Jplus*JzKet(1,1)) == 0
assert Jplus.matrix_element(1,1,1,1) == 0
assert Jplus.rewrite('xyz') == Jx + I*Jy
def test_H():
assert PIABHamiltonian('H').hilbert_space ==\
L2(Interval(S.NegativeInfinity,S.Infinity))
assert apply_operators(PIABHamiltonian('H')*PIABKet(n)) ==\
(n**2*pi**2*hbar**2)/(2*m*L**2)*PIABKet(n)