# 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 simple products of kets and bras inner products will be automatically identified and created:

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

But in more complex expressions, there is ambiguity in whether inner or outer products should be created:

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

A user can force the creation of a inner products in a complex expression by using parentheses to group the bra and ket:

```>>> 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