\(\int_{1}^{\infty} \frac{1}{x^2} \, dx = \lim_{{a \to \infty}} \int_{1}^{a} \frac{1}{x^2} \, dx\)
\(\int_{1}^{\infty} \frac{1}{x^2} \, dx = \lim_{{a \to \infty}} \left( -\frac{1}{x} \bigg|_{1}^{a} \right) = \lim_{{a \to \infty}} \left( -\frac{1}{a} + 1 \right) = 1\)
\(\hat{H} = -\frac{\hbar^2}{2m} \nabla^2 + \frac{1}{2} m \omega^2 x^2\)
