In the file linked below, I have written out a particular calculation of
a Gaussian integral, and would like to know if (6) in this file is is
correct. (If link does not work, right click to download and then
open.)

http://jayryablon.files.wordpress.co...al-correct.pdf

This is not rocket science nor is it particularly earthshaking. But, I
am having some conceptual trouble thinking about this integral (6) in
which the plane wave coefficient B=0, and would appreciate if someone
can help me straighten out my thinking about this.

Best regards,

Jay.
____________________________
Jay R. Yablon
Email:
co-moderator: sci.physics.foundations
Weblog: http://jayryablon.wordpress.com/
Web Site: http://home.nycap.rr.com/jry/FermionMass.htm

Hey again J-boy!

and would like to know if (6) in this file is is correct.
http://jayryablon.files.wordpress.co...alculation-of-...

Your eq(5) looks wrong. You can't just add the exponents
like that unless they commute. (d/dB doesn't commute with B^2).

This is not rocket science nor is it particularly
earthshaking. But, I am having some conceptual trouble
thinking about this integral (6) in which the plane wave
coefficient B=0, and would appreciate if someone can help me
straighten out my thinking about this.

You're guaranteed to get more help with this sort of boring
basic stuff over on www.physicsforums.com (try the quantum
physics forum). Also, it's latex-capable, so you don't need
to rely on auxiliary files like you're doing here on spr.

- LOL from Neuropulp!

P.S: I tried to reply to your previous posting, but it
attempt failed. Don't know why.

P.P.S: Try to think of a more original salutation than
"Pulp-boy". You can do better than that! :-) :-)
(Wrong gender, btw.)

On 15 May, 22:51, "Jay R. Yablon" wrote:
In the file linked below, I have written out a particular calculation of
a Gaussian integral, and would like to know if (6) in this file is is
correct. (If link does not work, right click to download and then
open.)

http://jayryablon.files.wordpress.co...alculation-of-...

This is not rocket science nor is it particularly earthshaking. But, I
am having some conceptual trouble thinking about this integral (6) in
which the plane wave coefficient B=0, and would appreciate if someone
can help me straighten out my thinking about this.

It would seem OK up to a point but it is not the way I would tackle
it.

Now e^x = 1+x+x^2/2! + x^3/3! + etc

Hence e^f(x) = 1+f(x)+f(x)^2/2! + f(x)^3/3! + etc

We know that Int (x^n)dx = x^(n+1)/(n+1) Hence if we have a power
series integration is trivial.

Now f(x) = -x^2 + V(x) we have a power series for f(x) and getting a
term by term evaluation is a matter of a term by term multiplication.
This gives your your equations for what you have labelled as C(n).

You can also constuct a series using Taylor's theorem, that is to say
you differentiate e^(f(x)) repeatedly.

You get f'(x)e^(f(x)) differentiating this again (f''(x) +
(f'(x)^2)e^(f(x))

Can you see one thing? The process of Taylor differentiation is
isomorphic with binomial multiplication (we would be surprised if it
wasn't).

You want clarification. I think the isomorphism of binomial
multiplication and Taylor's theorem does clarify things consiserably.

The physical meaning. There isn't a way to do things that isn't a
little bit messy.

- Ian Parker