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