I get the answer you describe for part (a) (that v=[0,ρω,0] which seems the obvious answer) if I use r=[ρ,0,0] not with r=[pcosψ,ρsinψ,0] is ω=[0,0,ω] unless I am really dumb and can't comput vector products (which is likely the problem b.t.w!) I am guessing that if I use the cartesian...
I am trying to work the following problem;
A rigid body is rotating about a fixed axis with a constant angular velocity ω. Take ω to lie entirely on th z-axis. Express r in cylindrical coordinates, and calculate;
a) v=ω × r
b)∇ × v
The answer to (a) is v=ψωρ and (b) is ∇ × v = 2ω...
I am required to show that the potential V= -Vo(1+iε) in the schrodinger equation results in stationary waves that represent exponentially decreasing plane waves. I am also required to calculate the absorption co-efficient.
My (inept) attempt at a solution;
I know that for a comlpex energy...
Sorry perhaps I was unclear, I know that the quadratic expansions do not equal where I am (was) trying to get.
Anyway I have since cracked it. The procedure is to use the prouct rule to get dG/dλ. You then multiply by eλbe-λb. You end up with
dG/dλ=[B+eλbAe-λb]G
The term eλbAe-λb] is an...
Just to expand on my attempt at a solution so far, which I think is barking up the wrong tree even though it seems close is;
1) taylor expand G(λ) at f(0) I get
G=1+λ[A+B]+λ2(A2+2AB+B2)/2!+...
=1+λ[A+B]+λ2(A+B)2/2!+λ3(A+B)3/3!
and then what makes this tempting is that differentiating...
[b]1. I am working through E.Merzbacher quantum mechanics. The problem is;
if G(λ) =eλAeλB for two operators A and B, show that
dG/dλ=[A+B+λ[A,B]/1!+λ2[A,[A,B]]/2!+....]G
[b]2. [A,B] is taken to mean AB-BA
[b]3. The only way I can think of proving this is by taylor expanding G(λ)...
No I was referring to my attempt at using latex (that clearly didn't work) I'm sorry I hope I didn't offend you. Anyway back to the problem.
I tried your suggestion of using t=cos(x). Surely then the upper limit will be zero, (since cos(0)=1) in which case the term (1-cos(x))^-1/3 will surely be...
Yes that's what I have been trying to write all along; thanks for clearing that up now we can proceed with trying to solve this! Clearly there are singularities at either end. How could you split range of the integral into two parts and then use a different variable change in each?
I am required to show that
(i)in the upper limit of very high energies, the Born and eikonal identities are identical.
(ii)that the eikonal amplitude satisfies the optical theorem.
Regarding (i) I think it will involve changing from an exponential to a trig(Euler's theorem) but I could be...
Ok let me try to re-enter this;
the integral I am trying to compute is;
[0]\int[/1][t]^{-2}[/3][(1-t)]^{-1}[/3]dt
I have never used latex before so bare with me if this is a disaster
I am required to write a program that uses Simpson's rule to evaluate ∫t**-2/3(1-t)**-1/3 dt from limits t=0 to t=1. The questions gives a hint to split the integral into two parts and use a change of variable to handle the singularities.
I really don't know where to begin. Is the choice of...