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An operator for representing the differential operator, i.e. d/dx

It is initialized by passing two arguments. The first is an arbitrary
expression that involves a function, such as ``Derivative(f(x), x)``. The
second is the function (e.g. ``f(x)``) which we are to replace with the
``Wavefunction`` that this ``DifferentialOperator`` is applied to.


src/s/y/sympy-HEAD/sympy/physics/quantum/cartesian.py   sympy(Download)
from sympy.physics.quantum.constants import hbar
from sympy.physics.quantum.hilbert import L2
from sympy.physics.quantum.operator import DifferentialOperator, HermitianOperator
from sympy.physics.quantum.state import Ket, Bra, State
        coord1 = states[0].momentum
        coord2 = states[1].momentum
        d = DifferentialOperator(coord1)
        delta = DiracDelta(coord1 - coord2)
        coord1 = states[0].position
        coord2 = states[1].position
        d = DifferentialOperator(coord1)
        delta = DiracDelta(coord1 - coord2)

src/s/y/sympy-HEAD/sympy/physics/quantum/tests/test_operator.py   sympy(Download)
from sympy.physics.quantum.dagger import Dagger
from sympy.physics.quantum.hilbert import HilbertSpace
from sympy.physics.quantum.operator import (Operator, UnitaryOperator,
                                            HermitianOperator, OuterProduct,
def test_differential_operator():
    x = Symbol('x')
    f = Function('f')
    d = DifferentialOperator(Derivative(f(x), x), f(x))
    g = Wavefunction(x**2, x)
    assert qapply(d*g) == Wavefunction(2*x, x)
    assert d.expr == Derivative(f(x), x)
    assert d.function == f(x)
    assert d.variables == (x,)
    assert diff(d, x) == DifferentialOperator(Derivative(f(x), x, 2), f(x))
    assert diff(d, x) == DifferentialOperator(Derivative(f(x), x, 2), f(x))
    d = DifferentialOperator(Derivative(f(x), x, 2), f(x))
    g = Wavefunction(x**3, x)
    assert qapply(d*g) == Wavefunction(6*x, x)
    assert d.expr == Derivative(f(x), x, 2)
    assert d.function == f(x)
    assert d.variables == (x,)
    assert diff(d, x) == DifferentialOperator(Derivative(f(x), x, 3), f(x))

src/s/y/sympy-HEAD/sympy/core/tests/test_args.py   sympy(Download)
def test_sympy__physics__quantum__operator__DifferentialOperator():
    from sympy.physics.quantum.operator import DifferentialOperator
    from sympy import Derivative, Function
    f = Function('f')
    assert _test_args(DifferentialOperator(1/x*Derivative(f(x), x), f(x)))

src/s/y/sympy-HEAD/sympy/physics/quantum/tests/test_printing.py   sympy(Download)
from sympy.physics.quantum.hilbert import ComplexSpace, FockSpace, HilbertSpace, L2
from sympy.physics.quantum.innerproduct import InnerProduct
from sympy.physics.quantum.operator import Operator, OuterProduct, DifferentialOperator
from sympy.physics.quantum.qexpr import QExpr
from sympy.physics.quantum.qubit import Qubit, IntQubit
    f = Function('f')
    x = symbols('x')
    d = DifferentialOperator(Derivative(f(x), x), f(x))
    op = OuterProduct(Ket(), Bra())
    assert str(a) == 'A'
def test_big_expr():
    f = Function('f')
    x = symbols('x')
    e1 = Dagger(AntiCommutator(Operator('A') + Operator('B'), Pow(DifferentialOperator(Derivative(f(x), x), f(x)), 3))*TensorProduct(Jz**2, Operator('A') + Operator('B')))*(JzBra(1, 0) + JzBra(1, 1))*(JzKet(0, 0) + JzKet(1, -1))
    e2 = Commutator(Jz**2, Operator('A') + Operator('B'))*AntiCommutator(Dagger(Operator('C')*Operator('D')), Operator('E').inv()**2)*Dagger(Commutator(Jz, J2))

src/s/y/sympy-HEAD/sympy/physics/quantum/tests/test_cartesian.py   sympy(Download)
    PositionKet3D, PositionBra3D
from sympy.physics.quantum.operator import DifferentialOperator
x, y, z, x_1, x_2, x_3, y_1, z_1 = symbols('x,y,z,x_1,x_2,x_3,y_1,z_1')
    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)
    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)