The dispersion relation of d e broglie waves includes the rest mass, but the schrodinger equation does not. A simplified discussion can be based on the wave equation. This means that photons, electrons possess both momentum as well as wavelength. The speed of the wave wavelength x frequency, say the frequency is 6. This equation simply relates the wave character and the particle character of an object. What is the magnitude of the velocity of this electron. A particle which is moving with high speed is associated with k. There must be a correct way of deriving it for electrons etc. For an object to have a wavelength, it must be moving. Apr 08, 2017 debroglie wavelength of relativistic particle.
Since this is a type of semiclassical approximation, it makes sense to look for a solution of schrodingers equation as a power series in. The debroglie wavelength the lorentz transformation had been postulated for electromagnetic waves before einstein developed special relativity. By analogy with the wave and particle behaviour of light that had already been established experimentally, the french. Strategy the wavelength of the electrons must equal the wavelength of the photons to give the. This equation shows that wavelength depends upon mass and velocity of light i. He received the 1929 nobel prize in physics for this work. Matter waves are a central part of the theory of quantum mechanics, being an example of. But in the end one cannot derive this relationship. The equation further explains that a beam of electrons can also be diffracted just like a beam of light.
Electron microscope is a common instrument illustrating this fact. Thus, every object in motion has a wavelike character. Equate the wavelength of an electron and the wavelength of an. This means that a microscope using electron matter waves instead of photon light waves can see much smaller things. By rearranging the momentum equation stated in the above section, we find a relationship between the wavelength. The total energy of moving particle is given by e k. Theory of anomalous magnetic moment and lamb shift of. The em waves were entirely consistent with relativity. Plancks investigation of the emission spectra of hot objects and the subsequent studies into the photoelectric effect had proven that light was capable of behaving both as a wave and as a particle. Quantum physics i, lecture note 4 mit opencourseware. This work is licensed under a creative commons attributionnoncommercialsharealike 4. It seemed reasonable to wonder if electrons could also have a dual waveparticle nature. The wave properties of matter are only observable for very small objects.
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