dq.position

position(dim: int, *, layout: Layout | None = None, hbar: float = 0.5) -> QArray

Returns the position operator \(x = \sqrt{\hbar/2}\,(a^\dag + a)\).

Parameters:

• dim –

  Dimension of the Hilbert space.

• layout –

  Matrix layout (dq.dense, dq.dia or None).

• hbar –

  Value of \(\hbar\) in the commutation relation \([\hat{x}, \hat{p}] = i\hbar\). Common choices are 0.5 (default), 1.0, and 2.0.

Returns:

• (qarray of shape (dim, dim)) –

  Position operator.

Examples:

>>> dq.position(3)
QArray: shape=(3, 3), dims=(3,), dtype=complex64, layout=dia, ndiags=2
[[    ⋅     0.5  +0.j     ⋅    ]
 [0.5  +0.j     ⋅     0.707+0.j]
 [    ⋅     0.707+0.j     ⋅    ]]