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I'm not an expert teacher or lecturer of chemistry. I was only a student from SMA NEGERI 15 SURABAYA who had been one of the Bronze Medalist Participants of Olimpiade Sains Nasional X (2011) of Chemistry In Manado, North Sulawesi, 11 - 16 September 2011 and graduated in 2012. Now, I'm studying at Universitas Airlangga in Surabaya, Indonesia. I do love chemistry and I would like to help them who had difficulties in studying chemistry. That's why, please understand me if you found some misconcepts in my entries. Suggestions are always necessary in order to develop this blog. And I'm sorry because my English isn't so well.

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Saturday, November 03, 2012

Kinetic Energy of a Particle in a Box


From its wave function, kinetic energy of a particle in a box can be expressed by the following equation:


Where Ψ* is an anti-wave function, Ψ is a wave function, and H is the Eigen Operator. The border of the integration can be expressed like the expression above by following illustration:



The Eigen Operator (1 Dimention) can be expanded as follows:
In the box, the potential energy of particle is assumed by Zero (0)


You already got the expression and its definitions, now let's try to solve a problem.
If a particle has a wave function that can be expressed by the following equation:


Now the question is: Determine the kinetic energy of that particle.


First, you have to know that the anti-wave function has the same value with the wave equation:

Now, let's calculate it!
Confuse? Just read it slowly.
 
Now for the integration, you also have to know how to integrate those equations by following expression:

Let's continue our calculation!




Thank You
 

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