Quantum theory of radiation

Emission and absorption of electromagnetic radiation by molecular systems takes place in transitions from an initial quantum state i) to a final state /). The dipole transition matrix element associated with such a transition is obtained from the wavefunctions of these states, ipfr) and 

In this expression, d3r stands for r2 dr sin 3 dS dq . The asterisk designates the complex conjugate. 

It is well known that classical intensities of dipoles emitting radiation of frequency v y = ( — Ef)/hc may be converted to quantum expressions by replacing in Eq. 2.62 the classical squared dipole moment q2rl by four times the squared dipole transition element, 

In this case, the subscripts i,f of P of frequency may be dropped in the equation. 

Einstein s A and B coefficients. Quantized systems, such as atoms and molecules, emit and absorb radiation of frequency vy = E — Ej /hc in transitions between states i) and j) of energy , Ej. Einstein assumed that the probability that a system in state i) will absorb a photon of energy hcvij is proportional to the density of radiative energy per frequency interval, u(vij) dv. The probability of absorbing a photon in the time interval dt is given by 

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Einstein A 1917 On the quantum theory of radiation Phys. Z. 18 121 Reprinted ter Haar D 1967 The Old Quantum Theory (New York Pergamon)... 

W. Heitler, The Quantum Theory of Radiation, Oxford University Press, London, second edition, 1944 page 157. 

In 1912, Einstein extended the concept of quantum theory of radiation to photochemical processes and stated that each quantum of radiation absorbed by molecule activates one molecule in the primary step of a photochemical process . This is known as Einstein law of photochemical equivalence. 

The Occurrence of Her mite Functions in Wave Mechanics. The Hcrmite functions which wc have discussed in the Inst section occur in the wave mechanical treatment of the harmonic oscillator1). Although this is a very simple mechanical system the analysis of its properties is of great importance because of its application to the quantum theory of radiation. 

R. E. Moss, Advanced molecular quantum mechanics. An Introduction to Relativistic Quantum Mechanics and the Quantum Theory of Radiation, Chapman Hall, London, 1973. 

We now consider the effect of exposing a system to electromagnetic radiation. Our treatment will involve approximations beyond that of replacing (3.13) with (3.16). A proper treatment of the interaction of radiation with matter must treat both the atom and the radiation field quantum-mechanically this gives what is called quantum field theory (or quantum electrodynamics). However, the quantum theory of radiation is beyond the scope of this book. We will treat the atom quantum-mechanically, but will treat the radiation field as a classical wave, ignoring its photon aspect. Thus our treatment is semiclassical. 

Solvay s desire to submit his work on the fundamental principles what he called gravito-materialitique to the attention of Europe s leading physicists prompted Nernst to envision an international conference on the current problems of kinetic theory of matter and the quantum theory of radiation. The idea struck an immediate responsive chord in Solvay s mind, and he charged Nernst to explore it further with Planck, Lorentz, Einstein, and the other prominent physicists. Nernst was quick to pursue the idea immediately on his return from Brussels to Berlin. 

Heitler, W. Quantum theory of Radiation. Oxford Clarendon Press 1954. 

This is reminiscent of Planck s formula for the energy of a photon. It comes as no surprise then that the quantum theory of radiation has the structure of an assembly of oscillators, with each oscillator representing a mode of electromagnetic waves of a specified frequency. 

The Rayleigh-Jeans picture of the radiation field as an ensemble of different modes of vibration confined to an enclosure was applied to the blackbody problem in Chapter 1. The quantum theory of radiation develops this correspondence more explicitly, identifying each mode of the electromagnetic field with an abstract harmonic oscillator of frequency coa- The Hamiltonian for the entire radiation field can be written... 

Heitler, W. (1954). The Quantum Theory of Radiations. Oxford Clarendon Press. 

Heitler, W. The quantum theory of radiation. 3rd edit., p. 196. London Oxford University Press 1954... 

In this chapter we have reviewed some results concerning the quantum multipole radiation. Although the representation of quantum electromagnetic radiation in terms of spherical waves of photons known since the first edition in 1936 of the famous book by Heitler on quantum theory of radiation [2], where this subject is discussed in the Appendix, this representation is not a widespread one. The spherical waves of photons are considered in very few advanced monographs on quantum optics [26]. The brilliant encyclopedic monographs [14,15] just touch on the subject. 

Further work on similar types of cells has been carried out, in which not only is use made of the Nernst Theorem but likewise of the Einstein theory of atomic heat of solids (as modified by Nernst and Lmdemann) This will be taken up after we have discussed Planck s Quantum Theory of radiation and Einstein s application of it to the heat capacity of solids (Vol. Ill)... 

The photoelectric effect conld not be explained by the wave theory of light. Einstein, however, made an extraordinary assumption. He snggested that a beam of light is really a stream of particles. These particles of light are now called photons. Using Planck s quantum theory of radiation as a starting point, Einstein deduced that... 

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