Calculate the first-order correction to the ground-state energy of a particle in a three dimensional box with the perturbation:
H^1 = V in the range
a/4 < x < 3a/4, b/4 < y < 3b/4 , c/4 < z < 3c/4 where H^1=0 otherwise V=hv
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This solution calculates the wave functions of the particle in the ground state and uses integration limits and trigonometric functions to determine the first-order correction to the ground state energy of a particle with the specific perturbation. All steps are shown with explanations.