test_cartesian.py 文件源码

def test_x():
    assert X.hilbert_space == L2(Interval(S.NegativeInfinity, S.Infinity))
    assert Commutator(X, Px).doit() == I*hbar
    assert qapply(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)) == DiracDelta(x - x_1)
    assert represent(XBra(x)) == DiracDelta(-x + x_1)
    assert XBra(x).position == x
    assert represent(XOp()*XKet()) == x*DiracDelta(x - x_2)
    assert represent(XOp()*XKet()*XBra('y')) == \
        x*DiracDelta(x - x_3)*DiracDelta(x_1 - y)
    assert represent(XBra("y")*XKet()) == DiracDelta(x - y)
    assert represent(
        XKet()*XBra()) == DiracDelta(x - x_2) * DiracDelta(x_1 - x)

    rep_p = represent(XOp(), basis=PxOp)
    assert rep_p == hbar*I*DiracDelta(px_1 - px_2)*DifferentialOperator(px_1)
    assert rep_p == represent(XOp(), basis=PxOp())
    assert rep_p == represent(XOp(), basis=PxKet)
    assert rep_p == represent(XOp(), basis=PxKet())

    assert represent(XOp()*PxKet(), basis=PxKet) == \
        hbar*I*DiracDelta(px - px_2)*DifferentialOperator(px)