Poincare constant for Gaussian distribution

Question

The minimum of constant $C$ to satisfy the following condition is called Poincare constant for a probability measure $\mu$. For any smooth function $f$ on $\mathbb{R}$, the relation $$\int_{-\infty}^\infty (f(x)-E[f])^2 \mu(dx) \le C \int_{-\infty}^\infty f'(x)^2 \mu(dx) $$ holds, where $E[f]$ is the expectation of $f(X)$. It seems that Poincare constant for 1-dimensional Gaussian distribution is known. However, I cannot find its value and its suitable reference. I am seeking the answer for this question.