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Problem about boundries in this solve of quantum problem
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hey opeth_35! 
(btw, we say "limit" or "bound" for a number … "boundary" is for a curve or a surface
)
the integral is over the whole of space, and it's in spherical coordinates,
so the limits are: r from 0 to ∞, θ from 0 to π, and φ from 0 to 2π
(i don't understand your second question, but maybe the answer is that they used one of the standard trigonometric identities … sin2θ = (1 - cos2θ)/2)
(btw, we say "limit" or "bound" for a number … "boundary" is for a curve or a surface
)the integral is over the whole of space, and it's in spherical coordinates,
so the limits are: r from 0 to ∞, θ from 0 to π, and φ from 0 to 2π
(i don't understand your second question, but maybe the answer is that they used one of the standard trigonometric identities … sin2θ = (1 - cos2θ)/2)