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...
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 =...