# Fyrimynd:Braket/doc

"Template:Dirac notation" redirects here.

This is for producing templates {{bra}}, {{ket}}, and {{bra-ket}}. It can also produce quantum state vectors in bra–ket notation, using wikicode, ideally with {{math}}, as an alternative to LaTeX in [itex] mode, but using this template ( {{braket}} ) is more clumsy than the simpler and more directly applicable {{bra}}, {{ket}}, and {{bra-ket}}.

## Application

There are three parameters, use as many as needed in this order:

1. Brackets: choose one of:
• bra (for a bra vector),
• ket (for a ket vector),
• bra-ket (for the inner product), or
2. Symbol 1:
• if 1 is set to bra or ket: enter the first symbol for the bra or ket,
• if 1 is set to bra-ket: enter the symbol for the bra part of the inner product
3. Symbol 2:
• if 1 is set to bra or ket: this parameter is not needed.
• if 1 is set to bra-ket: enter the symbol for the ket part of the inner product

If 1 is set to bra-ket, the symbols are entered in the order they are read, left to right. The symbols can of course be bold, italic, underlined, any unicode symbol, etc.

## Examples

Ket

A ket can be written: , that is `{{braket|ket|ψ}}`.

Using {{math}}, a ket can be written: , that is `{{math|{{braket|ket|ψ}}}}`.

Bra

A bra can be written: ψ| = , that is `{{braket|bra|ψ}} = {{braket|ket|ψ}}<sup>†</sup>`.

Using {{math}}, a bra can be written: ψ| = , that is `{{math|{{braket|bra|ψ}} {{=}} {{braket|ket|ψ}}<sup>†</sup>}}`.

Bra-ket

The inner product of the kets and can be written: ψ|ξ = ξ|ψ, that is `{{braket|bra-ket|ψ|ξ}} = {{braket|bra-ket|ξ|ψ}}<sup>†</sup>`.

Using {{math}}, the inner product of the kets and can be written: ψ|ξ = ξ|ψ, that is `{{math|{{braket|bra-ket|ψ|ξ}} {{=}} {{braket|bra-ket|ξ|ψ}}<sup>†</sup>}}`.

Outer products

The outer product of the kets and can be written: ξ| = [ψ|], that is `{{braket|ket|ψ}}{{braket|bra|ξ}} = [{{braket|ket|ξ}}{{braket|bra|ψ}}]<sup>†</sup>`.

Using {{math}}, the outer product of the kets and can be written: ξ| = [ψ|], that is `{{braket|ket|ψ}}{{braket|bra|ξ}} {{=}} [{{braket|ket|ξ}}{{braket|bra|ψ}}]<sup>†</sup>`.

Inner products including operators

The inner product of the kets and Ĥ is written using a bra and ket separately between the operator (there is no third parameter for the operator symbol):

ψ|Ĥ = ξ|Ĥ,

that is

`{{braket|bra|ψ}}''Ĥ''{{braket|ket|ξ}} = {{braket|bra|ξ}}''Ĥ''<sup>†</sup>{{braket|ket|ψ}}`.

Using {{math}}, the inner product of the kets and Ĥ is written using a bra and ket separately between the operator:

ψ|Ĥ = ξ|Ĥ,

that is

`{{math|{{braket|bra|ψ}}''Ĥ''{{braket|ket|ξ}} {{=}} {{braket|bra|ξ}}''Ĥ''<sup>†</sup>{{braket|ket|ψ}}}}`.
Schrödinger equation

In wiki-markup rather than LaTeX:

d/dt|Ψ(t) = Ĥ|Ψ(t) ↔ −Ψ(t)|d/dt = Ψ(t)|Ĥ

that is,

`{{math|''iħ''{{sfrac|''d''|''dt''}}{{braket|ket|Ψ(''t'')}} {{=}} ''Ĥ''{{braket|ket|Ψ(''t'')}} ↔ −''iħ''{{braket|bra|Ψ(''t'')}}{{sfrac|''d''|''dt''}} {{=}} {{braket|bra|Ψ(''t'')}}''Ĥ''<sup>†</sup>}}`
Tensor products

The tensor product of the kets and is written using the ket mode only (there is no paramter for tensor products):

|ξ, ψ,

that is

`{{braket|ket|ξ}}{{braket|ket|ψ}} ≡ {{braket|ket|ξ}}&otimes;{{braket|ket|ψ}} ≡ {{braket|ket|ξ, ψ}}`.

Using {{math}}, the tensor product of the kets and is written using the ket mode only:

|ξ, ψ,

that is

`{{math|{{braket|ket|ξ}}{{braket|ket|ψ}} ≡ {{braket|ket|ξ}}&otimes;{{braket|ket|ψ}} ≡ {{braket|ket|ξ, ψ}}}}`.