How can integration by parts simplify this integral?

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In summary, the function "R e^(-2r/a)*r^2 dr" represents a probability density function in quantum mechanics for finding an electron at a certain distance from the nucleus in a hydrogen atom. The "r" represents the distance from the nucleus, while the "a" represents the Bohr radius, a constant value used in the calculation. The value of "a" affects the shape and peak of the function, with a smaller value resulting in a tighter and taller peak, and a larger value resulting in a broader and shorter peak. This function is specifically applicable to hydrogen atoms, but variations can be used for other atoms.
  • #1
starbaj12
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from r to R e^(-2r/a)*r^2 dr

Thanks
 
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  • #2
starbaj12 said:
from r to R e^(-2r/a)*r^2 dr

Thanks

U're one lazy dude... Two times part integration,pay attention to signs and integration limits.
Daniel.
 
  • #3
Looks pretty standard to me.

Use "integration by parts", twice.

If you let u= r2 and dv= e-2r/a, then du= 2r dr and
v= -a/2 e-2r/a

Now you have an integral of e-2r/ar and integrating by parts again will give you an integral with just e-2r/a.
 

FAQ: How can integration by parts simplify this integral?

What does the function "R e^(-2r/a)*r^2 dr" represent?

The function represents a probability density function in quantum mechanics, specifically for finding an electron at a certain distance from the nucleus in a hydrogen atom.

What does the "r" represent in the function?

The "r" represents the distance from the nucleus in a hydrogen atom.

What is the significance of the "a" in the function?

The "a" represents the Bohr radius, which is a constant value used in the calculation of electron probability distribution in a hydrogen atom.

How does the value of "a" affect the function?

The value of "a" affects the shape and peak of the probability density function. A smaller value of "a" results in a tighter and taller peak, indicating a higher probability of finding the electron closer to the nucleus. Conversely, a larger value of "a" results in a broader and shorter peak, indicating a lower probability of finding the electron closer to the nucleus.

Is this function applicable to all atoms or just hydrogen?

This function is specifically applicable to hydrogen atoms, as it is based on the Bohr model of the atom. However, variations of this function can be used to represent the probability distribution of electrons in other atoms as well.

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