I m looking for a sequence $(f_j)\in C^\infty(\Bbb{R})$ such that

$$
\int^\infty_0\Big|\partial^2_r f_j+\frac{1}{r}\partial_r f_j+r^2f_j\Big|^2rdr\to 0,
$$ and

$$\int_{\Bbb{R^+}}|f_j(r)|^2 rdr=1\quad\forall j\in\Bbb{N}.$$

Could anybody help? Thanks in advance.