How I can write Hamiltonian by considering screening effect? Which book I can find formula:
Indeed, for seeing transition lines of ions in a plasma ; people solve shorodinger equation; I do not know how to write its Hamiltonian by considering screening effect? Is it important to consider Screening effect in this case??
In this case an effective screened potential could be used. Preferably, in the second quantization picture with the Fourier transformed (FT) effective potential equal to the FT potentail divided by the FT dielectric function.
It depends what you are studying and what you want to do. For instance if you have a plasma you can write the full Hamiltonian, including ionic and electronic kinetic and potential energies and their interaction (pure Coulomb) and screening will follow when you solve the equations. Or, alternative you can have a uniform (jellium ) neutralizing background; or you can write a Debye-type potential and study say the motion of an electron in the Debye-screened field of an ion. If you want dynamic screening you need the dielectric response as indicated in the previous post.
There are different possibilities. You could use directly the Debye (or Yukawa) potential V=q*exp(-r/ldh)/(r*r) where ldh is the Debye length. You can give a look to the book "Fundamental Aspects of plasma chemical physics: thermodynamics" By Capitelli et al or "Quantum Statistic of Nonideal Plasma" by Kremp et al, both published by springer.
For Hydrogen atom this problem has been solved, since 70's (Roussel, O'Connell Phys Rev A vol 9 pp 52). I have investigated the effects of the screen potential on thermodynamics in the paper (Capitelli et al Phys of Plasma 2008 vol 15 pp 115) See attached document.
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