Abstract Already from the systematic development of quantum mechanics have Kramers and Heisenberg2 so completely deduced the quantum theoretical dispersion equation that today the famous Raman Effect (“Smekal jumps”) can be quantitatively calculated. In addition, they mentioned another effect that until now has not yet been observed. In the light-quantum language it allows the following simple description:
Abstract Already from the systematic development of quantum mechanics have Kramers and Heisenberg2 so completely deduced the quantum theoretical dispersion equation that today the famous Raman Effect (“Smekal jumps”) can be quantitatively calculated. In addition, they mentioned another effect that until now has not yet been observed. In the light-quantum language it allows the following simple description:
The following notes introduce Quantum Mechanics at an advanced level addressing students of Physics, Mathematics, Chemistry and Electrical Engineering. The aim is to put mathematical concepts and techniques like the path integral, algebraic techniques, Lie algebras and representation theory at the readers disposal. For this purpose we attempt to motivate the various physical and mathematical concepts as well as provide detailed derivations and complete sample calculations. We have made every effort to include in the derivations all assumptions and all mathematical steps implied, avoiding omission of supposedly ‘trivial’ information. Much of the author’s writing effort went into a web of cross references accompanying the mathematical derivations such that the intelligent and diligent reader should be able to follow the text with relative ease, in particular, also when mathematically difficult material is presented. In fact, the author’s driving force has been his desire to pave the reader’s way into territories unchartered previously in most introductory textbooks, since few practitioners feel obliged to ease access to their field. Also the author embraced enthusiastically the potential of the TEX typesetting language to enhance the presentation of equations as to make the logical pattern behind the mathematics as transparent as possible. Any suggestion to improve the text in the respects mentioned are most welcome. It is obvious, that even though these notes attempt to serve the reader as much as was possible for the author, the main effort to follow the text and to master
It has been shown by Schr\"odinger and O. Klein that the Kramers-Heisenberg formulas for dispersion and incoherent scattering can both be obtained by an extension of Schr\"odinger's method for treating dispersion, the terms in the Hamiltonian involving squares of the potentials being neglected. The resulting formulas agree with those of Dirac. They are, however, inconvenient for calculations, as they contain summations with respect to all energy levels combining with the pair of levels under consideration, and thus imply complicated integrations when a continuous spectrum is present. This paper treats the problem of a hydrogen-like atom, acted on by light the wave-length of which is large compared to the size of the atom and the frequency of which is not too near a resonance frequency, and develops a method which obviates the necessity of integrating over the continuous range. It is an extension of the method used by one of us in treating the dispersion by atomic hydrogen. It is applied in detail to the first two levels of H. Formulas are derived for the intensities of the Smekal-Raman lines with a shift corresponding to the first absorption line.
If we have to go on with these damned quantum jumps, then I'm sorry that I ever got involved. E. Schrödinger Introduction I have borrowed the title of a characteristic paper by Schrödinger (Schrödinger, 1952). In it he contrasts the smooth evolution of the Schrödinger wavefunction with the erratic behaviour of the picture by which the wavefunction is usually supplemented, or ‘interpreted’, in the minds of most physicists. He objects in particular to the notion of ‘stationary states’, and above all to ‘quantum jumping’ between those states. He regards these concepts as hangovers from the old Bohr quantum theory, of 1913, and entirely unmotivated by anything in the mathematics of the new theory of 1926. He would like to regard the wavefunction itself as the complete picture, and completely determined by the Schrödinger equation, and so evolving smoothly without ‘quantum jumps’. Nor would he have ‘particles’ in the picture. At an early stage, he had tried to replace ‘particles’ by wavepackets (Schrödinger, 1926). But wavepackets diffuse. And the paper of 1952 ends, rather lamely, with the admission that Schrödinger does not see how, for the present, to account for particle tracks in track chambers … nor, more generally, for the definiteness, the particularity, of the world of experience, as compared with the indefiniteness, the waviness, of the wavefunction. It is the problem that he had had (Schrödinger, 1935 a ) with his cat. He thought that she could not be both dead and alive.
Abstract In two preliminary papers we have recorded the discovery that when monochromatic light is scattered in a transparent medium (be it gas, vapour, liquid, amorphous solid or crystal), the diffused radiation ceases to be monochromatic, and several new lines or sometimes bands (associated in many cases with a continuous spectrum) appear in the spectrograms of the diffused radiation. Further, the new radiations are, in general, strongly polarised. That the phenomenon is entirely distinct from what is usually known as fluorescence is clear from the fact that the effect is observed when both the exciting radiation and the new radiations generated by it are far removed from the characteristic ultra-violet and infra-red frequencies of the medium. As an illustration we may mention the case of transparent crystalline quartz in which the effect is very well shown with the 4358 A. U. line of mercury as the exciting line, the new lines also appearing in the indigo-blue region of the spectrum. Our preliminary studies have proved conclusively that the effect arises in the following way: The incident quantum of radiation is either scattered as a whole, in which case we have the classical scattering, or else is absorbed in part by the molecules of the medium, the remaining part appearing as a scattered quantum. The part absorbed shifts the molecule to a level of energy different from the initial state. The possibility of a process of this kind, in respect of the electronic state of an atom, was first contemplated by Smekal, and figures prominently in the theory of dispersion due to Kramers and Heisenberg, and in the papers of Schrödinger. Our experiments furnish definite proof of the possibility of such processes, and show that they may occur also in such complicated systems as the molecules of a vapour or a liquid or even in a complete crystal. In the series of papers of which this is the first our further studies of the new radiations will be discussed.