# \matrixel

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

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

## 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
\matrixel{a}{H}{b}
```

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

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

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

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

[Open in Playground](https://play.texform.dev/?input=%5Cmatrixel**%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
\matrixel{#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).

### [physics/matrixel-expand](https://texform.dev/rules/physics/matrixel-expand)

Expand matrix elements to explicit angle-bracket and bar fences.

Level: faithful. Fidelity: render.

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

→

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

```latex
\matrixel{n}{\hat{x}}{m}=x_{nm}
```

→

```latex
\left\langle n \right\vert \hat{x} \left\vert m \right\rangle=x_{nm}
```

## Equivalent forms

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

exact. 

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

exact. 

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

exact. 

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

exact. 

```latex
\mel
```

exact. 

## See also

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

## Test cases

### physics

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