In a similar way we can also define expectation values of functions \( f(x,t) \) as $$ \begin{equation*} \langle f(x,t)\rangle = \int_{-\infty}^{\infty}f(x,t)w(x,t)dx. \end{equation*} $$ The normalization condition $$ \begin{equation*} \int_{-\infty}^{\infty}w(x,t)dx=1 \end{equation*} $$ imposes significant constraints on \( w(x,t) \).