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 $|p⟩$ of the dimensionless momentum operator P in the number basis.

See position, momentum.

Difference equation:

$$\begin{array}{rl}{r}_1& =i\sqrt{2}p{r}_0,\\ \sqrt{k+1}{r}_{k+1}& =i\sqrt{2}p{r}_k+\sqrt{k}{r}_{k-1},\text{when}k>=1.\end{array}$$