Source code for sympy.physics.quantum.dagger

"""Hermitian conjugation."""

from sympy.core import Expr
from sympy.functions.elementary.complexes import adjoint

__all__ = [
    'Dagger'
]


[docs]class Dagger(adjoint): """General Hermitian conjugate operation. Take the Hermetian conjugate of an argument [1]_. For matrices this operation is equivalent to transpose and complex conjugate [2]_. Parameters ========== arg : Expr The sympy expression that we want to take the dagger of. Examples ======== Daggering various quantum objects: >>> from sympy.physics.quantum.dagger import Dagger >>> from sympy.physics.quantum.state import Ket, Bra >>> from sympy.physics.quantum.operator import Operator >>> Dagger(Ket('psi')) <psi| >>> Dagger(Bra('phi')) |phi> >>> Dagger(Operator('A')) Dagger(A) Inner and outer products:: >>> from sympy.physics.quantum import InnerProduct, OuterProduct >>> Dagger(InnerProduct(Bra('a'), Ket('b'))) <b|a> >>> Dagger(OuterProduct(Ket('a'), Bra('b'))) |b><a| Powers, sums and products:: >>> A = Operator('A') >>> B = Operator('B') >>> Dagger(A*B) Dagger(B)*Dagger(A) >>> Dagger(A+B) Dagger(A) + Dagger(B) >>> Dagger(A**2) Dagger(A)**2 Dagger also seamlessly handles complex numbers and matrices:: >>> from sympy import Matrix, I >>> m = Matrix([[1,I],[2,I]]) >>> m [1, I] [2, I] >>> Dagger(m) [ 1, 2] [-I, -I] References ========== .. [1] http://en.wikipedia.org/wiki/Hermitian_adjoint .. [2] http://en.wikipedia.org/wiki/Hermitian_transpose """ def __new__(cls, arg): if hasattr(arg, 'adjoint'): obj = arg.adjoint() elif hasattr(arg, 'conjugate') and hasattr(arg, 'transpose'): obj = arg.conjugate().transpose() if obj is not None: return obj return Expr.__new__(cls, arg)
adjoint.__name__ = "Dagger" adjoint._sympyrepr = lambda a, b: "Dagger(%s)" % b._print(a.args[0])