Need help fast Radial probablility density in ground state hydrogen

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SUMMARY

The discussion centers on the radial probability density of the ground state of the hydrogen atom, specifically the equation P(r)dr = |\psi|^2 4 \pi r^2 dr. The user is confused about discrepancies between different sources regarding the radial dependence of probability density. The sources referenced include a PowerPoint presentation from ASU and a Physics Forums thread. The user seeks clarification on why the two representations of radial probability density differ and requests detailed reasoning to resolve the confusion.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly wave functions.
  • Familiarity with spherical coordinates and their applications in physics.
  • Knowledge of the hydrogen atom's quantum states and their properties.
  • Basic grasp of probability density functions in quantum mechanics.
NEXT STEPS
  • Review the derivation of the radial probability density for the hydrogen atom.
  • Study the differences between wave functions in quantum mechanics and their interpretations.
  • Examine the implications of spherical coordinates in quantum systems.
  • Explore additional resources on quantum mechanics, such as textbooks or online lectures, focusing on the hydrogen atom.
USEFUL FOR

Students of quantum mechanics, physicists studying atomic structures, and educators seeking to clarify concepts related to the hydrogen atom's probability density.

Whazupp
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I'm working all alone with nobody to help me, and now I'm stuck! :(

I'd really appreciate it if you could help me out. I'm working with the ground state of the one electron hydrogen atom. Trying to determine the radial dependence on probability density. It should only depend on the radial coordinate and not on the other spherical coordinates.

I've got one book saying the the radial dependence of probability density is:

[tex]P(r)dr = |\psi|^2 4 \pi r^2 dr[/tex]

Now another says something along the lines of:

http://img222.imageshack.us/img222/5153/radialic9.jpg

I got these two from:

http://phy.asu.edu/phy361-alarcon/FALL06/lecture22_1109.ppt" (power point)

and

https://www.physicsforums.com/showthread.php?t=49807"

Now why aren't they the same? Please help.
 
Last edited by a moderator:
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We need to see your reasoning first.

Start with the probability density - how is it defined?
 

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