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A condition for Laplacian

Let $u\in L^{2}(\mathbb{R}^{2}) $ with $-\Delta(u) -c (x^{2}+y^{2})u \in L^{2}(\mathbb{R}^{2})$ where $c>0$. Is true $-\Delta u \in L^{2}(\mathbb{R}^{2})$? Thank you in advance.