Solving the Schrodinger Equation for Fusion Process | Integral Help

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Discussion Overview

The discussion revolves around solving the Schrödinger equation in the context of a fusion process, specifically focusing on an integral that arises during the solution process. The scope includes mathematical reasoning and integration techniques.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant presents the integral \(\int dx\sqrt{\frac{1}{x}-1}\) and seeks assistance in solving it.
  • A subsequent reply indicates that integration by parts leads to the integral \(\int dx\frac{1}{x\sqrt{x-1}}\) and mentions that the result is proportional to \(\text{atan}(\sqrt{x-1})\), questioning how to prove this relationship.
  • Another participant claims to have solved the integral using the substitution \(y=\sqrt{x-1}\).

Areas of Agreement / Disagreement

The discussion does not reach a consensus on the proof of the proportionality to the arctangent, as the initial question remains unaddressed in terms of verification.

Contextual Notes

The discussion includes assumptions about the validity of integration techniques and the physical interpretation of the results, which are not fully explored or resolved.

eoghan
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Hi all!
I'm trying to solve the Schrödinger equation for a fusion process. I came up with this integral
[tex] \int dx\sqrt{\frac{1}{x}-1}[/tex]
I can't see how to solve it... can you please give me an hint?

Thank you
 
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Ok... I applied the integration by part and now I have
[tex] \int dx\frac{1}{x\sqrt{x-1}}[/tex]
I know that the result is proportional to [itex]atan(\sqrt{x-1})[/itex] and this is also correct by a physical point of view. The problem is how to prove that the integral is proportional to the arctangent...
 
Ok... I got it! I made the substitution [itex]y=\sqrt{x-1}[/itex] and I finally solved the integral
 
Glad we could help!
 

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