- #1
Firben
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Homework Statement
Consider a one-dimensional linear harmonic oscillator perturbed by a Gaussian perturbation H' = λe-ax2. Calculate the first-order correction to the groundstate energy and to the energy of the first excited state
Homework Equations
ψn(x) = [itex]\frac{α}{√π*2n*n!}[/itex]1/2 * e-α2x2[itex]\frac{1}{2}[/itex]
E1n = <ψ0n|H'|ψ0n>
The Attempt at a Solution
E10 = <ψ00|H'|ψ00> =
∫[itex]\frac{α}{√π*2n*n!}[/itex]1/2 * e-α2x2[itex]\frac{1}{2}[/itex]*[itex]\frac{α}{√π*2n*n!}[/itex]1/2 * e-α2x2[itex]\frac{1}{2}[/itex]*H'* dx
Is this right ? What is α in this case ?