qit.ho.momentum_state¶
- qit.ho.momentum_state(p, n=30)¶
Momentum eigenstates of a harmonic oscillator.
- Parameters
q (float) – dimensionless momentum coordinate
n (int) – truncation dimension
- Returns
approximate momentum eigenstate
- Return type
array[complex]
Returns the n-dimensional approximation of the eigenstate \(\ket{p}\) of the dimensionless momentum operator P in the number basis.
Difference equation:
\[\begin{split}r_1 &= i \sqrt{2} \: p \: r_0,\\ \sqrt{k+1} \: r_{k+1} &= i \sqrt{2} \: p \: r_k +\sqrt{k} \: r_{k-1}, \qquad \text{when} \quad k >= 1.\end{split}\]