Dagger¶
Hermitian conjugation.
- class sympy.physics.quantum.dagger.Dagger(arg)[source]¶
General Hermitian conjugate operation.
- Parameters
arg : Expr
The sympy expression that we want to take the dagger of.
Explanation
Take the Hermetian conjugate of an argument [R627]. For matrices this operation is equivalent to transpose and complex conjugate [R628].
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 Matrix([ [1, I], [2, I]]) >>> Dagger(m) Matrix([ [ 1, 2], [-I, -I]])
References
