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First Dirichlet eigenvalue of the harmonic oscillator on a bounded interval $(-a,a)$?
Let $a>0$ be a fixed number and consider the Hermite operator (or harmonic oscillator) defined by
\begin{equation}
Hf(x)=x^2f(x)-f''(x)
\end{equation}
for any smooth function $f$ compactly ...
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