# \matrixelement

Used in quantum-mechanics bra-ket notation to write matrix elements such as ⟨a|H|b⟩.

https://texform.dev/latex/commands/matrixelement

## Metadata

| Field | Value |
| --- | --- |
| Topic | [Physics: bra-ket](https://texform.dev/latex/topics/physics-braket) |
| Packages | physics |
| Allowed mode | math |
| Tags |  |
| Commonality | low |
| Kind | prefix |

## Syntax

### physics

Argument specification: `s s m m m`

Used in quantum-mechanics bra-ket notation to write matrix elements such as ⟨a|H|b⟩.

## Examples

```latex
\matrixelement{a}{H}{b}
```

[Open in Playground](https://play.texform.dev/?input=%5Cmatrixelement%7Ba%7D%7BH%7D%7Bb%7D)

```latex
\matrixelement*{a}{H}{b}
```

[Open in Playground](https://play.texform.dev/?input=%5Cmatrixelement*%7Ba%7D%7BH%7D%7Bb%7D)

```latex
\matrixelement**{a}{H}{b}
```

[Open in Playground](https://play.texform.dev/?input=%5Cmatrixelement**%7Ba%7D%7BH%7D%7Bb%7D)

## Renderer support

| Package | MathJax | KaTeX | XeTeX |
| --- | --- | --- | --- |
| physics | full | none | full |

## In TeXForm

TeXForm parses this entry as prefix syntax; the package determines its argument specification.

### Expands to (physics)

```latex
\matrixelement{#1}{#2}{#3}
```

→

```latex
\left\langle{#1}\right\vert{#2}\left\vert{#3}\right\rangle
```

With one star: \langle{#1}\vert{#2}\vert{#3}\rangle (no auto-sizing). With two stars: \left\langle{#1}\middle\vert{#2}\middle\vert{#3}\right\rangle (middle delimiters).

## Equivalent forms

```latex
\matrixelement{#1}{#2}{#3} ≡ \left\langle{#1}\right\vert{#2}\left\vert{#3}\right\rangle
```

exact. 

```latex
\matrixelement*{#1}{#2}{#3} ≡ \langle{#1}\vert{#2}\vert{#3}\rangle
```

exact. 

```latex
\matrixelement**{#1}{#2}{#3} ≡ \left\langle{#1}\middle\vert{#2}\middle\vert{#3}\right\rangle
```

exact. 

```latex
\mel
```

exact. 

## See also

- [\\matrixel](https://texform.dev/latex/commands/matrixel)
- [\\mel](https://texform.dev/latex/commands/mel)

## Test cases

### physics

| Input | Case | MathJax | KaTeX | XeTeX |
| --- | --- | --- | --- | --- |
| \matrixelement{a}{b}{c} | Positive: baseline | Pass | Fail | Pass |
| \matrixelement*{a}{b}{c} | Positive: vary:s[0] | Pass | Fail | Pass |
| \matrixelement**{a}{b}{c} | Positive: maximal | Pass | Fail | Pass |
| \matrixelement a{b}{c} | Positive: bare[2] | Pass | Fail | Pass |
| \matrixelement{a}b{c} | Positive: bare[3] | Pass | Fail | Pass |
| \matrixelement{a}{b}c | Positive: bare[4] | Pass | Fail | Pass |