def test_3dpos():
assert Y.hilbert_space == L2(Interval(S.NegativeInfinity, S.Infinity))
assert Z.hilbert_space == L2(Interval(S.NegativeInfinity, S.Infinity))
test_ket = PositionKet3D(x, y, z)
assert qapply(X * test_ket) == x * test_ket
assert qapply(Y * test_ket) == y * test_ket
assert qapply(Z * test_ket) == z * test_ket
assert qapply(X * Y * test_ket) == x * y * test_ket
assert qapply(X * Y * Z * test_ket) == x * y * z * test_ket
assert qapply(Y * Z * test_ket) == y * z * test_ket
assert PositionKet3D() == test_ket
assert YOp() == Y
assert ZOp() == Z
assert PositionKet3D.dual_class() == PositionBra3D
assert PositionBra3D.dual_class() == PositionKet3D
other_ket = PositionKet3D(x_1, y_1, z_1)
assert (Dagger(other_ket)*test_ket).doit() == \
DiracDelta(x - x_1)*DiracDelta(y - y_1)*DiracDelta(z - z_1)
assert test_ket.position_x == x
assert test_ket.position_y == y
assert test_ket.position_z == z
assert other_ket.position_x == x_1
assert other_ket.position_y == y_1
assert other_ket.position_z == z_1
def test_states():
assert PIABKet(n).dual_class() == PIABBra
assert PIABKet(n).hilbert_space ==\
L2(Interval(S.NegativeInfinity,S.Infinity))
assert represent(PIABKet(n)) == sqrt(2 / L) * sin(n * pi * x / L)
assert (PIABBra(i) * PIABKet(j)).doit() == KroneckerDelta(i, j)
assert PIABBra(n).dual_class() == PIABKet
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)
def test_H():
assert PIABHamiltonian("H").hilbert_space == L2(
Interval(S.NegativeInfinity, S.Infinity)
)
assert qapply(PIABHamiltonian("H") * PIABKet(n)) == (
n ** 2 * pi ** 2 * hbar ** 2
) / (2 * m * L ** 2) * PIABKet(n)
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_p():
assert Px.hilbert_space == L2(Interval(S.NegativeInfinity, S.Infinity))
assert qapply(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)) == DiracDelta(px-px_1)
rep_x = represent(PxOp(), basis = XOp)
assert rep_x == -hbar*I*DiracDelta(x_1 - x_2)*DifferentialOperator(x_1)
assert rep_x == represent(PxOp(), basis = XOp())
assert rep_x == represent(PxOp(), basis = XKet)
assert rep_x == represent(PxOp(), basis = XKet())
assert represent(PxOp()*XKet(), basis=XKet) == \
-hbar*I*DiracDelta(x - x_2)*DifferentialOperator(x)
assert represent(XBra("y")*PxOp()*XKet(), basis=XKet) == \
-hbar*I*DiracDelta(x-y)*DifferentialOperator(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)