qit.ho.position_state

qit.ho.position_state(q, n=30)

Position eigenstates of a harmonic oscillator.

Parameters

• q (float) – dimensionless position coordinate

• n (int) – truncation dimension

Returns

approximate position eigenstate

Return type

array[complex]

Returns the n-dimensional approximation of the eigenstate $|q⟩$ of the dimensionless position operator Q in the number basis.

See position, momentum.

Difference equation:

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