Inner Product¶

Symbolic inner product.

class sympy.physics.quantum.innerproduct.InnerProduct(bra, ket)[source]¶

An unevaluated inner product between a Bra and a Ket [1].

Parameters:

bra : BraBase or subclass

The bra on the left side of the inner product.

ket : KetBase or subclass

The ket on the right side of the inner product.

Examples

Create an InnerProduct and check its properties:

>>> from sympy.physics.quantum import Bra, Ket
>>> b = Bra('b')
>>> k = Ket('k')
>>> ip = b*k
>>> ip
<b|k>
>>> ip.bra
<b|
>>> ip.ket
|k>

In quantum expressions, inner products will be automatically identified and created:

>>> b*k
<b|k>

In more complex expressions, where there is ambiguity in whether inner or outer products should be created, inner products have high priority:

>>> k*b*k*b
<b|k>*|k><b|

Notice how the inner product <b|k> moved to the left of the expression because inner products are commutative complex numbers.

References