Commutator¶
The commutator: [A,B] = A*B - B*A.
- class sympy.physics.quantum.commutator.Commutator(A, B)[source]¶
The standard commutator, in an unevaluated state.
- Parameters
A : Expr
The first argument of the commutator [A,B].
B : Expr
The second argument of the commutator [A,B].
Explanation
Evaluating a commutator is defined [R625] as:
[A, B] = A*B - B*A
. This class returns the commutator in an unevaluated form. To evaluate the commutator, use the.doit()
method.Canonical ordering of a commutator is
[A, B]
forA < B
. The arguments of the commutator are put into canonical order using__cmp__
. IfB < A
, then[B, A]
is returned as-[A, B]
.Examples
>>> from sympy.physics.quantum import Commutator, Dagger, Operator >>> from sympy.abc import x, y >>> A = Operator('A') >>> B = Operator('B') >>> C = Operator('C')
Create a commutator and use
.doit()
to evaluate it:>>> comm = Commutator(A, B) >>> comm [A,B] >>> comm.doit() A*B - B*A
The commutator orders it arguments in canonical order:
>>> comm = Commutator(B, A); comm -[A,B]
Commutative constants are factored out:
>>> Commutator(3*x*A, x*y*B) 3*x**2*y*[A,B]
Using
.expand(commutator=True)
, the standard commutator expansion rules can be applied:>>> Commutator(A+B, C).expand(commutator=True) [A,C] + [B,C] >>> Commutator(A, B+C).expand(commutator=True) [A,B] + [A,C] >>> Commutator(A*B, C).expand(commutator=True) [A,C]*B + A*[B,C] >>> Commutator(A, B*C).expand(commutator=True) [A,B]*C + B*[A,C]
Adjoint operations applied to the commutator are properly applied to the arguments:
>>> Dagger(Commutator(A, B)) -[Dagger(A),Dagger(B)]
References