1 / 15

Quantum Mechanics II: Homework Assignment #9 and #10 on Atomic Properties and Hydrogen Molecule Ion

This is a review of atomic properties in quantum mechanics, focusing on ionizing energy and binding energy. The homework assignments cover problems on electron configuration, hydrogen atom, and hydrogen molecule ion. The quiz asks about the most relevant parameter to optimize when using the variational principle for the ground state of a hydrogen molecule ion. The concept of LCAO technique and trial wave function are also discussed.

strandj
Download Presentation

Quantum Mechanics II: Homework Assignment #9 and #10 on Atomic Properties and Hydrogen Molecule Ion

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Physics 452 Quantum mechanics II Winter 2012 Karine Chesnel

  2. Phys 452 Homework Tuesday Feb14: assignment # 9 Pb 7.6, 7.7, 7.15, 7.16 Thursday Feb 16: assignment # 10 Pb 7.8, 7.9, 7.13, 7.17

  3. Phys 452 Review of atomic properties Ionizing energy: to extract or add 1 electron at a time Binding energy: to extract all the electrons from atom (equal in norm to energy of ground state)

  4. Phys 452 electron H atom H atom Hydrogen molecule ion H2+

  5. Phys 452 Quiz 14 When looking for the ground state of hydrogen molecule ion using the variational principle, what is the most relevant parameter to optimize? • The apparent Z due to screening effect • The reduced mass of the system • The distance between the electron and first nucleus • The distance between the electron and first nucleus • The distance between the two nuclei

  6. Phys 452 Hydrogen molecule ion H2+ electron the distance R is fixed R is going to be our parameter in the variational principle 3-bodies system… Hard to Solve! Assumption: the two nuclei are at rest

  7. Phys 452 Hydrogen molecule ion H2+ electron 3-bodies system… Hamiltonian?

  8. Phys 452 Hydrogen molecule ion H2+ LCAO Technique (linear combination of atomic orbitals) Trial wave function? electron

  9. Phys 452 Hydrogen molecule ion H2+ electron Normalization Overlap integral Trial wave function?

  10. Phys 452 Small Overlap Great Overlap Hydrogen molecule ion H2+ Overlap integral The normalization coefficient A will depend on the distance R!

  11. Phys 452 Hydrogen molecule ion H2+ calculation Overlap integral

  12. Phys 452 Normalization coefficient Hydrogen molecule ion H2+ Trial wave function: where

  13. Phys 452 Hydrogen molecule ion H2+ Hydrogen Hamiltonian with first nucleus Hydrogen Hamiltonian with second nucleus Cross terms Use the trial wave function: To calculate

  14. Hydrogen molecule ion H2+ Phys 452 Direct integral D exchange integral X Pb. 7.8

  15. Hydrogen molecule ion H2+ Phys 452 Finally…! where

More Related