Editing Weyl algebra (section)

=== Representation ===
The Weyl algebra <math>A_n</math> can be concretely constructed as a [[Algebra representation|representation]].

In the differential operator representation, similar to Schrödinger's canonical quantization, let <math>q_j</math> be represented by multiplication on the left by <math>x_j</math>, and let <math>p_j</math> be represented by differentiation on the left by <math>\partial_{x_j}</math>.

In the matrix representation, similar to the [[matrix mechanics]], <math>
A_1
</math> is represented by{{sfn|Coutinho|1997|pp=598–599}}<math display="block">
P=\begin{bmatrix}
0 & 1 & 0 & 0 & \cdots \\
0 & 0 & 2 & 0 & \cdots \\
0 & 0 & 0 & 3 & \cdots \\
\vdots & \vdots & \vdots & \vdots & \ddots
\end{bmatrix}, \quad Q=\begin{bmatrix}
0 & 0 & 0 & 0 & \ldots \\
1 & 0 & 0 & 0 & \cdots \\
0 & 1 & 0 & 0 & \cdots \\
\vdots & \vdots & \vdots & \vdots & \ddots
\end{bmatrix}
</math>