Schrodinger equation quantum electrodynamics

The relativistic many-electron Hamiltonian cannot be written in closed form it may be derived perturbatively from quantum electrodynamics [1]. The simplest form is the Dirac-Coulomb (DC) Hamiltonian, where the nonrelativistic one-electron terms in the Schrodinger equation are replaced by the one-electron Dirac operator hj). 

A negative imaginary potential in the time-independent Schrodinger equation absorbs the particle flux, thus violating the law of conservation of flux, which is satisfied for real potentials [12,13]. Then, the quantum electrodynamical phenomenon of pair annihilation can be represented by particle loss due to an effective absorption potential H = —zVabs since the exact mechanism of positron loss is totally irrelevant to the study of the atomic processes in consideration [9,10,14-16]. The only important aspect of pair annihilation for the present purpose is the correct description of the loss rate. The absorption potential H is proportional to the delta function 5 (r) of the e+-e distance vector r (Section 4.2). 

Aside from relativistic and quantum electrodynamic effects, a single molecule in free space is completely described by the Schrodinger equation = (8-2.1)... 

This second point of view can be illustrated by an example from the late 1940 s that will play an important role in this chapter. At that time the Schrodinger equation was well established, and its relativistic generalization, the Dirac equation, appeared to describe the spectrum of hydrogen perfectly, though the question of how to apply the Dirac equation to many-electron systems was still open. However, when more precise experiments were carried out, most notably by Lamb and Retherford [1], a small disagreement with theory was found. The attempt to understand this new physics stimulated theoretical efforts that led to the modern form of the first quantum field theory. Quantum Electrodynamics (QED). This small shift, which removes the Dirac degeneracy between the 2si/2 and states, known as the Lamb shift, is an example of a radiative correction. 

The Schrodinger equation (more precisely the refined version incorporating both relativity and quantum electrodynamics), and those obtained from it, describe the physical and chemical features of the hydrogen atom with an accuracy limited only by the precision to which the fundamental constants required are known. Unfortunately, the hydrogen atom is the only chemical structure for which the Schrodinger equation can be solved exactly everything else requires approximation. For small atoms and very small molecules the approximations can be very good, but for any... 

In this book the interaction between fields and molecules is treated in a semi-classical fashion. Quantum mechanics is used for the description of the molecule, whereas the treatment of the electromagnetic fields is based on classical electromagnetism. A complete quantmn mechanical description using quantmn electrodynamics is beyond the scope of this presentation, although we will make use of the correct value of the electronic g-factor as given by quantum electrodynamics. Furthermore, only ab initio methods derived from the non-relativistic Schrodinger equation are discussed. Nevertheless, the Dirac equation is briefly discussed in order to introduce the electronic spin via the Pauli Hamiltonian. 

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