Type:

Other

Description:

"), the sum over all ... states for an ... -subshell of hydrogen-like orbitals reduces to a spherically symmetrical function: ... . For a pure Coulomb potential with any nuclear charge ... , the different ... states for a given ... are also degenerate. The author has derived a generalization of Unsöld's theorem, an explicit form for the sum over both ... and ... for hydrogenic orbitals, namely, ... , where ... is a Whittaker function that can alternatively be written as ... . We can define a radial distribution function (RDF) for a completely filled ... -shell by ... . This is normalized according to ... , reflecting the orbital degeneracy of the energy level ... . In this Demonstration the function ... is plotted for selected values of ... (1 to 10) and ... (1 to 25). L. S. Bartell has derived the classical analog of ... , which, in accordance with Bohr's correspondence principle, approaches the quantum result in the limit ... . The checkbox produces a red plot of the classical function. The generalized Unsöld theorem has found several theoretical applications, including derivation of the canonical Coulomb partition function, density-functional computations, supersymmetry, and study of high- ... Rydberg states of atoms.

Subjects:

    Education Levels:

      Keywords:

      EUN,LOM,LRE4,work-cmr-id:398013,http://demonstrations.wolfram.com:http://demonstrations.wolfram.com/GeneralizedUnsoeldTheoremForHydrogenicFunctions/,ilox,learning resource exchange,LRE metadata application profile,LRE

      Language:

      Access Privileges:

      Public - Available to anyone

      License Deed:

      Creative Commons Attribution 3.0

      Collections:

      None
      This resource has not yet been aligned.
      Curriki Rating
      'NR' - This resource has not been rated
      NR
      'NR' - This resource has not been rated

      This resource has not yet been reviewed.

      Not Rated Yet.

      Non-profit Tax ID # 203478467