A quantum-mechanical model is developed which reproduces the atomic and molecular energy spectra of the many-body Pauli equation with Coulomb interactions and external electro- and magneto-static fields without putting these interactions in by hand. The model also describes the emission of electromagnetic radiation / photons with the right frequencies. Photons feature without invoking ``second quantizing'' the classical Maxwell equations. The model also suggests that Lorentz covariance emerges through a law of large numbers from a microscopic model which is not itself fundamentally Lorentz covariant.
On semi-relativistic quantum mechanics of N-body systems composed of nuclei, electrons, and photons
A quantum-mechanical model is developed which reproduces the atomic and molecular energy spectra of the many-body Pauli equation with Coulomb interactions and external electro- and magneto-static fields without putting these interactions in by hand. The model also describes the emission of electromagnetic radiation / photons with the right frequencies. Photons feature without invoking ``second quantizing'' the classical Maxwell equations. The model also suggests that Lorentz covariance emerges through a law of large numbers from a microscopic model which is not itself fundamentally Lorentz covariant.
Semi-relativistic N-body quantum mechanics of electrons and photons, with fixed nuclei
It is argued that by the end of the 1920s a quantum-mechanical model could have been in place, that not only produces the atomic and molecular energy levels of the many-body Pauli equation with Coulomb interactions and external classical electro- and magneto-static fields without putting these interactions in by hand, but that also accurately describes the interaction of charged particles with electromagnetic radiation, in particular the transitions between atomic or molecular energy levels associated with emission or absorption of radiation. This model suggests a re-interpretation of Maxwell's electromagnetic field equations on spacetime as quantum-mechanical expected values of wave equations on time X configuration space for photons and electrons. The creation / annihilation formalism for photons emerges without invoking second-quantizing the classical Maxwell equations, and without involving the concept of creation / annihilation, thus suggesting an alternative physical interpretation of this formalism. Furthermore, the model suggests that Lorentz covariance of macroscopic physics models emerges through a law of large numbers from a fundamental microscopic model that is not itself Lorentz covariant.
This paper presents a realistic model that describes radiation-matter interactions. This is achieved by a generalization of first quantization, where the Maxwell equations are interpreted as the electromagnetic component of the Schroedinger equation. This picture is complemented by the consideration of electrons and photons as real particles in three-dimensional space, following guiding conditions derived from the particle-wave-functions to which they are associated. The guiding condition for the electron is taken from Bohmian mechanics, while the photon velocity is defined as the ratio between the Poynting vector and the electromagnetic energy density. The case of many particles is considered, taking into account their statistical properties. The formalism is applied to a two level system, providing a satisfactory description for spontaneous emission, Lamb shift, scattering, absorption, dispersion, resonance fluorescence and vacuum fields. This model adequately describes quantum jumps by the entanglement between the photon and the atomic system and it will prove to be very useful in the simulation of quantum devices for quantum computers and quantum information systems. A possible relativistic generalization is presented, together with its relationship to QED.
This chapter considers an atom as a quantum mechanical system. But the electromagnetic radiation will be treated as classical waves described by the Maxwell equations. The treatment is called semi-classical. Quantum mechanics describes an atom as a quantized system with a set of discrete energy levels. Each energy level is designated by a set of quantum numbers like the principal quantum of the Rydberg level and the quantum numbers representing the orbital, spin and total angular momentum. A molecule will have a different set of quantum numbers arising from its rotational and vibrational motions. Atoms in a solid have energy levels in the form of a band. The observed spectrum due to spontaneous emission from a collection of atoms is not monochromatic, but it is spread over a certain range of frequencies. The absorption spectrum also shows that the atom does not absorb at a single frequency, but it is spread over a band of frequencies around the resonance frequency.
We describe here the coherent formulation of electromagnetism in the nonrelativistic quantummechanical many-body theory. We use the mathematical frame of the field theory and its quantization in the spirit of the QED. This is necessary because of the manifold of misinterpretations emerging from the hystorical development of quantum mechanics, starting from the Schrödinger equation of a single particle in the presence of given electromagnetic fields, followed by the many-body theories of many charged identical particles having just Coulomb interactions inspired from the classical electromagnetic theory of point-like charges. However, this later is known to be inconsistent due to the self-interaction. This way could not be continued further to include properly the magnetic forces between the charged particles and lead to a lot of confusion about the interpretation of the magnetic field in the Hamiltonian, as well as about the gauge invariance. We emphasize the importance of the distinction between the applied (external fields) and the field in the matter. All these problems are length properly solved within the non-relativistic QED, nevertheless the confusion dominates in all the problems related to the magnetic properties of the solid state.
We investigate in this chapter the general problem of the interaction of an atom (or a molecule) and a classical electromagnetic field. Its importance derives firstly from the fact that a large part of our knowledge of atoms is obtained from a study of the radiation they absorb or emit (we shall consider equally visible radiation and radio-frequency and X-rays) and, secondly, that the interaction with matter modifies the propagation of the electromagnetic field itself, notably through absorption, refraction or scattering. The interactions of atoms with light therefore encompass a vast range of physical effects that we could not hope to cover adequately in a single chapter. In this chapter we shall therefore present the fundamental features of the interaction of an atom, which will be treated quantum mechanically, with a classical electromagnetic field, that is an electromagnetic field described by real electric and magnetic vectors obeying Maxwell's equations. A rigorous description of the atom–light interaction would have to take into account the quantum nature of light. This we shall leave to Chapter 6. It turns out, nevertheless, that many important results can be obtained from the semi-classical viewpoint adopted here (although it is perhaps more appropriate to refer to this treatment as ‘semi-quantized’).
We treat the interaction between an electromagnetic radiation bath and a material system in the semi-classical picture: the radiation is treated according to the Maxwell equations, but the process of emission/absorption is described through the concept of a photon; on the other hand, the material system is modelled according to quantum mechanics, assuming a discrete two-level energy spectrum. This very simple model allows one to elaborate the elementary theory of the absorption/emission coefficients, both for the spontaneous and for the stimulated processes which will be described within the electric dipole approximation. Selection rules for allowed transitions are eventually obtained and the nature of high-order transition is briefly outlined. Finally, a qualitative description of the light amplification by stimulated emission of radiation is presented.