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Atomic units and Hydrogenic Atoms

Hydrogen energy levels diagram - drawn for l-values separately. A proper scan from a textbook
can be found in our older notes on this page in ../spectra/
QUANTUM NUMBERS.
Selection rules. Originate from transition probabilities proportional to < final | d | initial >, and the fact that these
integrals are (most often) zero unless the "rule" is satisfied ( d-dipole, vector, L=1; from it delta L must be one )
1-drawing_hydrogen_spectra.png
Here we discussed the relation of energy level diagram to the "line spectrum", as function of wavelengths
Conservation of angular momentum in classical physics - from one of our texts
1B-conserve_L_angular_Classical.png
RELATED:   KEPLER PROBLEM - toy http://web.ift.uib.no/AMOS/kepler/   (program running in browser)
In the following picture we commented a version of hydrogen level diagram from
../spectra/
especially the various representations of the transition radiation - wavelengths, energy, wavenumber
2-Hydrogen-spectrum.png
For discussion of these representations - see older link Wavelengths - relations
Atomic units - Constants - atomic units
3-atomic-units-derived-defined.png
Atomic units - Constants - atomic units  - the following is a capture to PNG from the PDF in the link
4-atomic_units.png
Atomic units - Constants - atomic units  - the following is a capture to PNG from the PDF in the link
5-some-constants.png

We also discussed shortly the so called Gaussian units, or rather the question of "permittivity of vacuum".
In both parts of these lecture we use the view that "permittivity of vacuum" has no physical reality and is
simply connected to a somewhat unfortunate historical developement. For practical purposes we naturally
use the SI units, as they are defined by physical phenomena. See also ../2004.09.08/
in particular
../2004.09.08/table2.jpg and
../2004.09.08/table3.jpg

There is a useful file from 2006 - "online record" of a lecture by one of the students
../tex_2006.08.29/
the PDF file from there is  2006.08.29.pdf

What we have touched (or should touch) in these 2 lectures:

Hydrogen - like atoms

-  CENTRAL POTENTIAL   ->  Angular momentum conservation
- Classical   -  Quantum Theory Angular momentum  ---  Y_LM  
             Spherical harmonics

Separation of variables -  classical, r, theta, phi

Separation of variables - Conservation of (all components ) of angular momentum vector
(classical)

Separation of variables - Conservation of LENGTH of angular momentum vector, or L-squared
(QUANTUM)

Radial waves general, hydrogen radial eigenfunctions

Quantum results - Quantum numbers    n, l, m  Spectra, Energy level diagrams

Atomic Units; Virial Theorem  (wikipedia);

Johnson's book - Lectures on Atomic Physics

 Spectra
History of Atoms - Atomic models (Christmas pudding with raisins)
Rutherford; Bohr

Schrödinger equation; Wolfgang Pauli

Hydrogen Atom
wavefunctions

Atomic Units; Virial Theorem  (wikipedia);

Rydberg Atom

Orbitals

Electromagnetism - Relations, Units

Physics formulas are stories in miniature
(so is most of math)

Closed trajectories, ONLY Kepler and HO,

(statistics of the trajectories - QM )   (Circular flat potential well - all closed trajectories ???? NO !!! )

Physics and Computers (world wide web is a child of physics)

Fun: Victoria Hart on YouTube (math art)

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