Recent content by marineric

I think I got it. The solutions manual integrated from 0 to ∞, and multiplied by 2 because of symmetry (to get the -∞ to 0 part)

i) the domain is for all x and t > 0? ii) the bounds of the integral are from 0 to ∞

Homework Statement A particle of mass m is in the state ψ(x,t) = Ae-a[mx2/h-bar)+it] Find A Homework Equations I know that to normalize a wave function I should use ∫ψ2 = 1 The Attempt at a Solution The book gives the solution as 1 = 2abs(A)2∫ e-2amx2/h-bar) dx My question is...

Ok so attempt at a solution: ∫∫ 3\vec{r} r^{2}sinθdθd\phi limits are 0 to 2∏ for θ, and 0 to ∏/2 for \phi, or I could just do 3r^3 time the surface area of a hemisphere, which is 2*∏*r^2, so, 6*∏*a^5? for divergence... do I just take the divergence in spherical coordinates and multiply...

for the stokes' theorem part, would it just be the ∇\times\vec{v} times the area of the square, which is a^2?

oh, right, minus sign.. so it equals a^2/2 for the top line, and i just do it similarly for all the other sides? do i have to do it in the same order (clockwise)?

wait hold on \vec{r} = (d\vec{x}, 0, 0) ?? then it would be the integral from -a/2 to a/2 of y*dx where y = a/2? but that's (a/2*x) from -a/2 to a/2 ... which equals zero?

Ok well I'll try the top line of the square and you can tell me what I'm doing wrong. From left to right: \oint d\vec{r}\cdot\vec{v} from -a/2 to a/2 \vec{v} = (y,0,0) \vec{r} = (x, a/2, 0) d\vec{r} = (1, 0, 0) d\vec{r}\cdot\vec{v} = y but aren't the y limits a/2 to a/2...

Homework Statement Please evaluate the integral \oint d\vec{A}\cdot\vec{v}, where \vec{v} = 3\vec{r} and S is a hemisphere defined by |\vec{r}| \leqa and z ≥ 0, a) directly by surface integration. b) using the divergence theorem. Homework Equations -Divergence theorem in...

Homework Statement Please evaluate the line integral \oint dr\cdot\vec{v}, where \vec{v} = (y, 0, 0) along the curve C that is a square in the xy-plane of side length a center at \vec{r} = 0 a) by direct integration b) by Stokes' theoremHomework Equations Stokes' theorem: \oint V \cdot dr =...