One simply assumes that the allowed bohr orbits arise because the electron matter waves interfere constructively when an integral number of wavelengths exactly. Contents list of figures iii preface to german translation v introduction 1 historical survey 2 chapter 1. As davisson and germer state in their 1928 followup paper, these results, including the failure of the data to satisfy the bragg formula, are. Note that for our focus on nonrelativistic particles the energy eis determined by the momentum through the relation p. The compton schwarzschild correspondence from extended. We use the heisenberg uncertainly relation text eq. To overcome the shortcomings of bohrs atomic model, attempts were made to develop a more general model for atoms. In the same context of the minkowski fourvectors formalism, we also discuss the phase and the group.
This means that the electronic copies of the journal can always be downloaded and redistributed by any person free of charge. In this article we investigate certain inconsistencies in its formulation. But in the end one cannot derive this relationship. We assume that the wave packet is a possible model of particle. Quantum physics i, lecture note 4 mit opencourseware.
A wave of definite single wavelength extends all over space. Comptons formula established that an electromagnetic wave can behave like a particle of light when interacting with matter. G p thompson independently carried out the same experiment. Planck, arthur compton, niels bohr, and many others laid the foundations for the theory. For matter waves, this group velocity is the velocity u of the particle. Bohr postulated that angular momentum of an electron revolving around the nucleus as quantized. Express the wavelength of the electron as a function of.
Matter waves istituto nazionale di fisica nucleare. His father j j thompson had shown that electrons were particles, the son showed that they were waves. He had been troubled by a curious contradiction arising from einsteins special theory of relativity. Matter waves are a central part of the theory of quantum mechanics, being an example of. By borns probability interpretation this means that the electron is not localised in any finite region of. In case of a photon, if it is assumed to have wave character, its energy is given by. The wavelength of the wave associated with any material particle was calculated by analogy with photon as follows.
Solved problems on matter waves university of british. Bohrs model failed to explain many concepts related to the spectrum of different atoms and splitting of spectral lines in magnetic and electric field. Phase velocity and group velocity for beginners in the first section of this paper i derive the formulas for the phase velocity and group velocity as a function of the total relativistic energy and the momentum of a particle. Wave theory tells us that a wave carries its energy with the group velocity. Since the equation is linear, any superposition of plane wave solutions with di.
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