AndroidRemoteController/python/py/Lib/site-packages/sympy/physics/quantum/fermion.py

"""Fermionic quantum operators."""

from sympy.core.numbers import Integer
from sympy.core.singleton import S
from sympy.physics.quantum import Operator
from sympy.physics.quantum import HilbertSpace, Ket, Bra
from sympy.functions.special.tensor_functions import KroneckerDelta


__all__ = [
    'FermionOp',
    'FermionFockKet',
    'FermionFockBra'
]


class FermionOp(Operator):
    """A fermionic operator that satisfies {c, Dagger(c)} == 1.

    Parameters
    ==========

    name : str
        A string that labels the fermionic mode.

    annihilation : bool
        A bool that indicates if the fermionic operator is an annihilation
        (True, default value) or creation operator (False)

    Examples
    ========

    >>> from sympy.physics.quantum import Dagger, AntiCommutator
    >>> from sympy.physics.quantum.fermion import FermionOp
    >>> c = FermionOp("c")
    >>> AntiCommutator(c, Dagger(c)).doit()
    1
    """
    @property
    def name(self):
        return self.args[0]

    @property
    def is_annihilation(self):
        return bool(self.args[1])

    @classmethod
    def default_args(self):
        return ("c", True)

    def __new__(cls, *args, **hints):
        if not len(args) in [1, 2]:
            raise ValueError('1 or 2 parameters expected, got %s' % args)

        if len(args) == 1:
            args = (args[0], S.One)

        if len(args) == 2:
            args = (args[0], Integer(args[1]))

        return Operator.__new__(cls, *args)

    def _eval_commutator_FermionOp(self, other, **hints):
        if 'independent' in hints and hints['independent']:
            # [c, d] = 0
            return S.Zero

        return None

    def _eval_anticommutator_FermionOp(self, other, **hints):
        if self.name == other.name:
            # {a^\dagger, a} = 1
            if not self.is_annihilation and other.is_annihilation:
                return S.One

        elif 'independent' in hints and hints['independent']:
            # {c, d} = 2 * c * d, because [c, d] = 0 for independent operators
            return 2 * self * other

        return None

    def _eval_anticommutator_BosonOp(self, other, **hints):
        # because fermions and bosons commute
        return 2 * self * other

    def _eval_commutator_BosonOp(self, other, **hints):
        return S.Zero

    def _eval_adjoint(self):
        return FermionOp(str(self.name), not self.is_annihilation)

    def _print_contents_latex(self, printer, *args):
        if self.is_annihilation:
            return r'{%s}' % str(self.name)
        else:
            return r'{{%s}^\dagger}' % str(self.name)

    def _print_contents(self, printer, *args):
        if self.is_annihilation:
            return r'%s' % str(self.name)
        else:
            return r'Dagger(%s)' % str(self.name)

    def _print_contents_pretty(self, printer, *args):
        from sympy.printing.pretty.stringpict import prettyForm
        pform = printer._print(self.args[0], *args)
        if self.is_annihilation:
            return pform
        else:
            return pform**prettyForm('\N{DAGGER}')

    def _eval_power(self, exp):
        from sympy.core.singleton import S
        if exp == 0:
            return S.One
        elif exp == 1:
            return self
        elif (exp > 1) == True and exp.is_integer == True:
            return S.Zero
        elif (exp < 0) == True or exp.is_integer == False:
            raise ValueError("Fermionic operators can only be raised to a"
                " positive integer power")
        return Operator._eval_power(self, exp)

class FermionFockKet(Ket):
    """Fock state ket for a fermionic mode.

    Parameters
    ==========

    n : Number
        The Fock state number.

    """

    def __new__(cls, n):
        if n not in (0, 1):
            raise ValueError("n must be 0 or 1")
        return Ket.__new__(cls, n)

    @property
    def n(self):
        return self.label[0]

    @classmethod
    def dual_class(self):
        return FermionFockBra

    @classmethod
    def _eval_hilbert_space(cls, label):
        return HilbertSpace()

    def _eval_innerproduct_FermionFockBra(self, bra, **hints):
        return KroneckerDelta(self.n, bra.n)

    def _apply_from_right_to_FermionOp(self, op, **options):
        if op.is_annihilation:
            if self.n == 1:
                return FermionFockKet(0)
            else:
                return S.Zero
        else:
            if self.n == 0:
                return FermionFockKet(1)
            else:
                return S.Zero


class FermionFockBra(Bra):
    """Fock state bra for a fermionic mode.

    Parameters
    ==========

    n : Number
        The Fock state number.

    """

    def __new__(cls, n):
        if n not in (0, 1):
            raise ValueError("n must be 0 or 1")
        return Bra.__new__(cls, n)

    @property
    def n(self):
        return self.label[0]

    @classmethod
    def dual_class(self):
        return FermionFockKet