Lowest-order correction for the bendulum

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eman2009
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what is the lowest-order correction to the ground state for the pendulum with small angle?
 
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[tex]cos(x)=1-x^2/2!+x^4/4!-...[/tex]
[tex]\delta E\propto<\Psi_0\mid x^4\mid\Psi_0>[/tex]