Anticommutator¶
The anti-commutator: {A,B} = A*B + B*A
.
-
class
sympy.physics.quantum.anticommutator.
AntiCommutator
[source]¶ The standard anticommutator, in an unevaluated state.
Evaluating an anticommutator is defined [R410] as:
{A, B} = A*B + B*A
. This class returns the anticommutator in an unevaluated form. To evaluate the anticommutator, use the.doit()
method.Cannonical ordering of an anticommutator is
{A, B}
forA < B
. The arguments of the anticommutator are put into canonical order using__cmp__
. IfB < A
, then{A, B}
is returned as{B, A}
.Parameters: A : Expr
The first argument of the anticommutator {A,B}.
B : Expr
The second argument of the anticommutator {A,B}.
References
[R410] (1, 2) http://en.wikipedia.org/wiki/Commutator Examples
>>> from sympy import symbols >>> from sympy.physics.quantum import AntiCommutator >>> from sympy.physics.quantum import Operator, Dagger >>> x, y = symbols('x,y') >>> A = Operator('A') >>> B = Operator('B')
Create an anticommutator and use
doit()
to multiply them out.>>> ac = AntiCommutator(A,B); ac {A,B} >>> ac.doit() A*B + B*A
The commutator orders it arguments in canonical order:
>>> ac = AntiCommutator(B,A); ac {A,B}
Commutative constants are factored out:
>>> AntiCommutator(3*x*A,x*y*B) 3*x**2*y*{A,B}
Adjoint operations applied to the anticommutator are properly applied to the arguments:
>>> Dagger(AntiCommutator(A,B)) {Dagger(A),Dagger(B)}