Template:Langle/doc

This is the left-handed angular bracket used for writing averages or bra–ket notation, with other applications primarily in mathematics and physics, for use when inline html rendering is desired rather than TeX rendering.

This is used in the braket template. When creating bra or ket vectors, or inner products, use Braket to save the trouble of typing &amp;#124; (for the pipe symbol), langle, or rangle every time.

Examples

 * Bras

The superposition of states can be written ⟨p| + ⟨q| + ⟨χ| + ⟨ψ|, which is inline with the text.

Another superposition of states: ⟨P| + ⟨Q| + ⟨Φ| + ⟨Ψ|, again inline.

The superposition of states can be written ⟨p| + ⟨q| + ⟨χ| + ⟨ψ|, which is inline with the text.

Another superposition of states: ⟨P| + ⟨Q| + ⟨Φ| + ⟨Ψ|, again inline.


 * Tables (also hidden boxes)

Due to the vertical bar | used in template coding, the html code &amp;#124; must be used when bra–ket notation is used in tables, else some parts will not show up because of code interference.

The correct way:

and the wrong way:

The correct way:

and the wrong way:


 * In conjunction with rangle:

One sum of inner products is ⟨p|q⟩ + ⟨χ|ψ⟩, a real number.

A sum of average values could be ⟨P|E|Q⟩ + ⟨Φ|p|Ψ⟩, another real number.

One sum of inner products is ⟨p|q⟩ + ⟨χ|ψ⟩, a real number.

A sum of average values could be ⟨P|E|Q⟩ + ⟨Φ|p|Ψ⟩, another real number.

The average of a quantity q may be written ⟨q⟩. The root mean square is then √⟨q2⟩, i.e. square every value, then average, then take the root.

The average of a quantity q may be written ⟨q⟩. The root mean square is then √⟨q2⟩, i.e. square every value, then average, then take the root.