Answered: 8.10 Apply the variation function = er… | bartleby

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8.10 Apply the variation function = er to the hydrogen atom. Choose the parameter c (which is
real) to minimize the variational integral, and calculate the percent error in the ground-state energy.
int:
-2π
[ ø*ødr = [²" ["* "*°
φάτ
0
JO
=
: 2 (277)
e-2cr² sino drdodo
ofe
*Âødt =
=
e-2cr² dr
ħ²
· S0₁ | - ²2 μ₁²
-2π
e-2cr] dr [" sinode [2" de
- (c²r²e-2cr -2cre-2cr) - Ze¹2 re-2cr dr
Zer21
= 2 (2π) [-1² (2-2) - 202²]
8c3
4c²

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