Template:Braket/doc

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"Template:Dirac notation" redirects here.

This is for producing quantum state vectors in bra–ket notation, using wikicode, ideally with {{math}}, as an alternative to LaTeX in <math> mode.

Application

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

  1. Brackets: choose one of:
  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 braket or ketbra: enter the symbol for the bra part of the inner product, or ket part of the outer product.
  3. Symbol 2:
    • if 1 is set to bra or ket: this parameter is not needed.
    • if 1 is set to braket or ketbra: enter the symbol for the ket part of the inner product, or bra part of the outer product.

If 1 is set to braket or ketbra, 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: Template:Rangle, that is {{braket|ket|ψ}}.

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

Bra

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

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

Braket

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

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

Ketbra

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

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

Inner products including operators

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

⟨ψ|ĤTemplate:Rangle = ⟨ξ|ĤTemplate:Rangle,

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 Template:Rangle and ĤTemplate:Rangle is written using a bra and ket seperatley between the operator:

⟨ψ|ĤTemplate:Rangle = ⟨ξ|ĤTemplate:Rangle,

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:

Template:Sfrac|Ψ(t)Template:Rangle = Ĥ|Ψ(t)Template:Rangle ↔ −⟨Ψ(t)|Template:Sfrac = ⟨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 Template:Rangle and Template:Rangle is written using the ket mode only (there is no paramter for tensor products):

Template:RangleTemplate:RangleTemplate:RangleTemplate:Rangle|ξ, ψTemplate:Rangle,

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 Template:Rangle and Template:Rangle is written using the ket mode only:

Template:RangleTemplate:RangleTemplate:RangleTemplate:Rangle|ξ, ψTemplate:Rangle,

that is

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

See also