How do I compute these inner products;

$(\Delta x)^2 = \frac{\int_R \!x^2\psi_m\psi_mdx}{\int_R \!\psi_m\psi_mdx}$

$(\Delta p)^2 = \frac{\int_R \!\psi_m\frac{d^2}{dx^2}\psi_mdx}{\int_R \!\psi_m\psi_mdx}$

Where $\psi(x) = h(x)e^{-x^2/2}$

$h_0 = 1$

$h_1 = 2x$

$h_2 = 2x^2-1$

$h_3 = \frac{4x^3}{3}-2x$

and how do I compute:

$\Delta x\Delta p$

  • $\begingroup$ It is far easier to compute these things using ladder operators. $\endgroup$ – jobe Feb 24 at 13:11

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