Vehicle-cpp/hkpc/software/sympy/physics/quantum/tests/test_state.py

from sympy.core.add import Add
from sympy.core.function import diff
from sympy.core.mul import Mul
from sympy.core.numbers import (I, Integer, Rational, oo, pi)
from sympy.core.power import Pow
from sympy.core.singleton import S
from sympy.core.symbol import (Symbol, symbols)
from sympy.core.sympify import sympify
from sympy.functions.elementary.complexes import conjugate
from sympy.functions.elementary.miscellaneous import sqrt
from sympy.functions.elementary.trigonometric import sin
from sympy.testing.pytest import raises

from sympy.physics.quantum.dagger import Dagger
from sympy.physics.quantum.qexpr import QExpr
from sympy.physics.quantum.state import (
    Ket, Bra, TimeDepKet, TimeDepBra,
    KetBase, BraBase, StateBase, Wavefunction,
    OrthogonalKet, OrthogonalBra
)
from sympy.physics.quantum.hilbert import HilbertSpace

x, y, t = symbols('x,y,t')


class CustomKet(Ket):
    @classmethod
    def default_args(self):
        return ("test",)


class CustomKetMultipleLabels(Ket):
    @classmethod
    def default_args(self):
        return ("r", "theta", "phi")


class CustomTimeDepKet(TimeDepKet):
    @classmethod
    def default_args(self):
        return ("test", "t")


class CustomTimeDepKetMultipleLabels(TimeDepKet):
    @classmethod
    def default_args(self):
        return ("r", "theta", "phi", "t")


def test_ket():
    k = Ket('0')

    assert isinstance(k, Ket)
    assert isinstance(k, KetBase)
    assert isinstance(k, StateBase)
    assert isinstance(k, QExpr)

    assert k.label == (Symbol('0'),)
    assert k.hilbert_space == HilbertSpace()
    assert k.is_commutative is False

    # Make sure this doesn't get converted to the number pi.
    k = Ket('pi')
    assert k.label == (Symbol('pi'),)

    k = Ket(x, y)
    assert k.label == (x, y)
    assert k.hilbert_space == HilbertSpace()
    assert k.is_commutative is False

    assert k.dual_class() == Bra
    assert k.dual == Bra(x, y)
    assert k.subs(x, y) == Ket(y, y)

    k = CustomKet()
    assert k == CustomKet("test")

    k = CustomKetMultipleLabels()
    assert k == CustomKetMultipleLabels("r", "theta", "phi")

    assert Ket() == Ket('psi')


def test_bra():
    b = Bra('0')

    assert isinstance(b, Bra)
    assert isinstance(b, BraBase)
    assert isinstance(b, StateBase)
    assert isinstance(b, QExpr)

    assert b.label == (Symbol('0'),)
    assert b.hilbert_space == HilbertSpace()
    assert b.is_commutative is False

    # Make sure this doesn't get converted to the number pi.
    b = Bra('pi')
    assert b.label == (Symbol('pi'),)

    b = Bra(x, y)
    assert b.label == (x, y)
    assert b.hilbert_space == HilbertSpace()
    assert b.is_commutative is False

    assert b.dual_class() == Ket
    assert b.dual == Ket(x, y)
    assert b.subs(x, y) == Bra(y, y)

    assert Bra() == Bra('psi')


def test_ops():
    k0 = Ket(0)
    k1 = Ket(1)
    k = 2*I*k0 - (x/sqrt(2))*k1
    assert k == Add(Mul(2, I, k0),
        Mul(Rational(-1, 2), x, Pow(2, S.Half), k1))


def test_time_dep_ket():
    k = TimeDepKet(0, t)

    assert isinstance(k, TimeDepKet)
    assert isinstance(k, KetBase)
    assert isinstance(k, StateBase)
    assert isinstance(k, QExpr)

    assert k.label == (Integer(0),)
    assert k.args == (Integer(0), t)
    assert k.time == t

    assert k.dual_class() == TimeDepBra
    assert k.dual == TimeDepBra(0, t)

    assert k.subs(t, 2) == TimeDepKet(0, 2)

    k = TimeDepKet(x, 0.5)
    assert k.label == (x,)
    assert k.args == (x, sympify(0.5))

    k = CustomTimeDepKet()
    assert k.label == (Symbol("test"),)
    assert k.time == Symbol("t")
    assert k == CustomTimeDepKet("test", "t")

    k = CustomTimeDepKetMultipleLabels()
    assert k.label == (Symbol("r"), Symbol("theta"), Symbol("phi"))
    assert k.time == Symbol("t")
    assert k == CustomTimeDepKetMultipleLabels("r", "theta", "phi", "t")

    assert TimeDepKet() == TimeDepKet("psi", "t")


def test_time_dep_bra():
    b = TimeDepBra(0, t)

    assert isinstance(b, TimeDepBra)
    assert isinstance(b, BraBase)
    assert isinstance(b, StateBase)
    assert isinstance(b, QExpr)

    assert b.label == (Integer(0),)
    assert b.args == (Integer(0), t)
    assert b.time == t

    assert b.dual_class() == TimeDepKet
    assert b.dual == TimeDepKet(0, t)

    k = TimeDepBra(x, 0.5)
    assert k.label == (x,)
    assert k.args == (x, sympify(0.5))

    assert TimeDepBra() == TimeDepBra("psi", "t")


def test_bra_ket_dagger():
    x = symbols('x', complex=True)
    k = Ket('k')
    b = Bra('b')
    assert Dagger(k) == Bra('k')
    assert Dagger(b) == Ket('b')
    assert Dagger(k).is_commutative is False

    k2 = Ket('k2')
    e = 2*I*k + x*k2
    assert Dagger(e) == conjugate(x)*Dagger(k2) - 2*I*Dagger(k)


def test_wavefunction():
    x, y = symbols('x y', real=True)
    L = symbols('L', positive=True)
    n = symbols('n', integer=True, positive=True)

    f = Wavefunction(x**2, x)
    p = f.prob()
    lims = f.limits

    assert f.is_normalized is False
    assert f.norm is oo
    assert f(10) == 100
    assert p(10) == 10000
    assert lims[x] == (-oo, oo)
    assert diff(f, x) == Wavefunction(2*x, x)
    raises(NotImplementedError, lambda: f.normalize())
    assert conjugate(f) == Wavefunction(conjugate(f.expr), x)
    assert conjugate(f) == Dagger(f)

    g = Wavefunction(x**2*y + y**2*x, (x, 0, 1), (y, 0, 2))
    lims_g = g.limits

    assert lims_g[x] == (0, 1)
    assert lims_g[y] == (0, 2)
    assert g.is_normalized is False
    assert g.norm == sqrt(42)/3
    assert g(2, 4) == 0
    assert g(1, 1) == 2
    assert diff(diff(g, x), y) == Wavefunction(2*x + 2*y, (x, 0, 1), (y, 0, 2))
    assert conjugate(g) == Wavefunction(conjugate(g.expr), *g.args[1:])
    assert conjugate(g) == Dagger(g)

    h = Wavefunction(sqrt(5)*x**2, (x, 0, 1))
    assert h.is_normalized is True
    assert h.normalize() == h
    assert conjugate(h) == Wavefunction(conjugate(h.expr), (x, 0, 1))
    assert conjugate(h) == Dagger(h)

    piab = Wavefunction(sin(n*pi*x/L), (x, 0, L))
    assert piab.norm == sqrt(L/2)
    assert piab(L + 1) == 0
    assert piab(0.5) == sin(0.5*n*pi/L)
    assert piab(0.5, n=1, L=1) == sin(0.5*pi)
    assert piab.normalize() == \
        Wavefunction(sqrt(2)/sqrt(L)*sin(n*pi*x/L), (x, 0, L))
    assert conjugate(piab) == Wavefunction(conjugate(piab.expr), (x, 0, L))
    assert conjugate(piab) == Dagger(piab)

    k = Wavefunction(x**2, 'x')
    assert type(k.variables[0]) == Symbol

def test_orthogonal_states():
    braket = OrthogonalBra(x) * OrthogonalKet(x)
    assert braket.doit() == 1

    braket = OrthogonalBra(x) * OrthogonalKet(x+1)
    assert braket.doit() == 0

    braket = OrthogonalBra(x) * OrthogonalKet(y)
    assert braket.doit() == braket