- #1

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## Homework Statement

I need to minimize the function Etrial[a]

trial[x_] := E^(-a*x^2)

Etrial[a_] :=

NIntegrate[1/2*D[trial[x], x]^2 + x^4*trial[x]^2, {x, -\[Infinity], \[Infinity]}]/

NIntegrate[trial[x]^2, {x, -\[Infinity], \[Infinity]}]

## Homework Equations

## The Attempt at a Solution

I have used NMinimize[Etrial[a],a] and Minimize[Etrial[a],a], as well as FindMiminum[Etrial[a],{a,.5}], since when I plot it, the minimum is pretty obviously around .7, so I arbitrarily chose .5 as a close starting point.