Quantum Mechanics Integral Trouble

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Homework Help Overview

The discussion revolves around an integral problem in quantum mechanics, specifically integrating the function \( x^2 \sin^2\left(\frac{n \pi x}{a}\right) \) over the interval from 0 to \( a \).

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster expresses difficulty in finding a solution despite consulting various integral tables. Some participants suggest rewriting the integral using a trigonometric identity and integrating by parts, while others provide resources for further exploration.

Discussion Status

The discussion includes attempts to clarify the integral setup and explore different methods of integration. While some guidance has been offered regarding the approach, there is no explicit consensus on the best method to solve the integral.

Contextual Notes

The original poster mentions a time constraint, having struggled with the problem for several weeks, and indicates that they have been advised to seek external resources.

jakePHYS
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1. Problem: int[(x^2)*(sin^2 (n*Pi*x/a)] from 0 to a

3. Physics teacher tells me to just look it up. I've wrestled with every table of integrals I can find (web, library, my books), but I'm still hung up.
 
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Write it as x^2*sin(k*x) where k is n*pi/a. First use the trig identity sin^2(kx)=(1-cos(2kx))/2. Then to integrate something like x^2*cos(2kx) you just have to integrate by parts twice. It's not the easiest integral in the world, but it's not the hardest either.
 
Thnx

:biggrin: This has been vexing me for 3 1/2 weeks now! THANK YOU! :biggrin:
 

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