Help with 2nd derivative please.



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Topic: Science > Physics
User: "Zinc Potterman delete digits to reply"
Date: 19 Jan 2005 07:11:26 AM
Object: Help with 2nd derivative please.
Help with 2nd derivative in physics problem please.
I am trying to follow a derivation and am stuck with this step.
If p=r/a, then du/dr = (1/a).du/dp (which i think I'm OK with)
and d2u/dr2 = (1/a)^2.d2u/dp2 (which I'm not)
(2's are powers here of course)
I'm not sure if it is relevant but earlier on in the text a substiitutuion
is used
u = r.psi(r) where psi is a function of r
Thanks
Zinc
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User: "Bjoern Feuerbacher"

Title: Re: Help with 2nd derivative please. 19 Jan 2005 08:58:26 AM
Zinc Potterman wrote:

Help with 2nd derivative in physics problem please.

I am trying to follow a derivation and am stuck with this step.

If p=r/a, then du/dr = (1/a).du/dp (which i think I'm OK with)

and d2u/dr2 = (1/a)^2.d2u/dp2 (which I'm not)

Why not?
d^2u/dr^2 = d/dr (du/dr)
= 1/a d/dr (du/dp)
= 1/a dp/dr d/dp (du/dp)
= 1/a 1/a d^2u/dp^2
= (1/a)^2 d^2u/dp^2
Where is the problem?

(2's are powers here of course)

Commonly denoted on usenet with an "^".

I'm not sure if it is relevant but earlier on in the text a substiitutuion
is used u = r.psi(r) where psi is a function of r

No, not relevant.
Apparently you are studying the Schroedinger equation
for spherically symmetric systems?
Bye,
Bjoern
.


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