Perturbative Treatment on Diatomic Hydrogen Molecule

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SUMMARY

The discussion centers on solving the perturbative treatment of the diatomic hydrogen molecule and its ion, referencing Pauling and Wilson's "Introduction to Quantum Mechanics" (1935). Key pages include 340 for the hydrogen molecule, 353 for excited states, and 327 for the hydrogen molecular ion. The Hylleraas variational approach is highlighted as the most accurate method for two-electron systems, outperforming perturbative calculations historically. Participants express a need for additional resources and insights on the topic.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with perturbation theory
  • Knowledge of the Hylleraas variational method
  • Access to Pauling and Wilson's "Introduction to Quantum Mechanics"
NEXT STEPS
  • Study the Hylleraas variational approach in detail
  • Review perturbation theory applications in quantum mechanics
  • Explore the excited states of diatomic molecules
  • Investigate computational methods for quantum systems
USEFUL FOR

Students and researchers in quantum mechanics, physicists focusing on molecular systems, and anyone interested in advanced computational methods for diatomic molecules.

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Hello Everyone! I need help on this topic. Can anyone provide me some details on how to solve the problem? Thanks..
 
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As I recall, the hydrogen molecule (and maybe also the hydrogen molecular ion) problems are solved in the quantum mechanics book by Pauling and Wilson.
Bob S

[added] Pauling and Wilson, Introduction to Quantum Mechanics, Mcgraw Hill (1935). See the following pages
Hydrogen molecule, page 340
Excited states of hydrogen molecule, page 353
Hydrogen molecule ion, page 327
 
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As an aside, the best method (as in - most accurate for the computational complexity) is the now seldom-seen Hylleraas variational approach (applied to helium in 1929), which works for two electrons but not that well for many more. The method was used to calculate hydrogen http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JCPSA6000001000012000825000001&idtype=cvips&gifs=yes" , with a result that was far better than perturbatory calculations could do at that time.
 
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alxm said:
Hey thanks for the link. I think the file has the information i need. Unfortunately i don't have an access to download the file. =) Just in case you have another link to that file perhaps you can post it. =)
 
Last edited by a moderator:
Bob S said:
As I recall, the hydrogen molecule (and maybe also the hydrogen molecular ion) problems are solved in the quantum mechanics book by Pauling and Wilson.
Bob S

[added] Pauling and Wilson, Introduction to Quantum Mechanics, Mcgraw Hill (1935). See the following pages
Hydrogen molecule, page 340
Excited states of hydrogen molecule, page 353
Hydrogen molecule ion, page 327
Thanks! I just borrowed that book and I will read it. I'll try to understand the book. I will post some questions just in case I can't understand some parts of it. =) Thanks again. Just in case you have any other info about the topic, please feel free to post it because it would really be a great help. =)
 

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