Template: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 mode, but using this template ( ⟨|⟩ ) is more clumsy than the simpler and more directly applicable 🇧🇷, ⟩, and ⟨|⟩.

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

 Brackets: choose one of:  Symbol 1:  Symbol 2:  
 * bra (for a bra vector),
 * ket (for a ket vector),
 * bra-ket (for the inner product), or
 * 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
 * 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: $⟨|ψ⟩$, that is.

Using math, a ket can be written: $⟨$, that is.


 * Bra

A bra can be written: $⟨|ψ⟩$ = $⟨ψ|$†, that is.

Using math, a bra can be written: $⟨$, that is.


 * Bra-ket

The inner product of the kets $⟨|ψ⟩$ and $⟨ψ|$ can be written: $⟨|ψ⟩$ = $⟨|ξ⟩$†, that is.

Using math, the inner product of the kets $= ⟨$ and $= ⟨$ can be written: $⟨$, that is.


 * Outer products

The outer product of the kets $⟨|ψ⟩$ and $⟨ψ|ξ⟩$ can be written: $⟨ξ|ψ⟩$$⟨ψ|ξ⟩$ = [$⟨ξ|ψ⟩$$⟨|ξ⟩$]†, that is.

Using math, the outer product of the kets $⟨$ and $ξ⟩ = ⟨ξ$ can be written: $ξ⟩ = ⟨ξ$, that is.


 * Inner products including operators

The inner product of the kets $⟨|ψ⟩$ and Ĥ$⟨|ψ⟩$ is written using a bra and ket separately between the operator (there is no third parameter for the operator symbol):
 * $⟨ξ|$Ĥ$⟨|ξ⟩$ = $⟨ψ|$Ĥ†$⟨|ψ⟩$,

that is

Using math, the inner product of the kets $⟨$ and $⟨$ is written using a bra and ket separately between the operator:

that is

In wiki-markup rather than LaTeX:
 * Schrödinger equation:

that is,


 * Tensor products:

The tensor product of the kets $⟨ξ|$ and $⟨|ξ⟩$ is written using the ket mode only (there is no parameter for tensor products):
 * $⟨ψ|$$⟨|ψ⟩$ ≡ $⟨ξ|$ &otimes; $⟨|ξ⟩$ ≡ $⟨ψ|$,

that is

Using math, the tensor product of the kets $ψ⟩⟨ξ$ and $⟨$ is written using the ket mode only:

that is