More specifically, we demonstrate that there is just one way, according to special relativity, to relate the finite energy and momentum of a corpuscle with the characteristics of a plane wave, frequency, wave vector and amplitude. 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. In 1924, lewis debroglie proposed that matter has dual characteristic just like radiation. According to debroglie hypothesis, the energy of the universe is in the form of matter and radiation. Equation 11 connects the module of the momentum p of a particle with the wavelength. By rearranging the momentum equation stated in the above section, we find a relationship between the wavelength. Pdf a charged photon and its lightspeed helical trajectory form a surprising new solution to the. The debroglie equations can be derived from the einsteins famous equation of energymass equivalence and planks theory of quantum radiation. The wave properties of matter are only observable for very small objects. It seemed reasonable to wonder if electrons could also have a dual waveparticle nature. Very low mass particles moving at speed less than that of light behaves like a particle and wave. Before i derive the equation, it is important to understand the debroglie hypothesis which i am sure.
The debroglie wavelength will be our primary physics input for the development of quantum mechanics. It basically describes the wave nature of the electron. This means that photons, electrons possess both momentum as well as wavelength. But in the end one cannot derive this relationship. For an object to have a wavelength, it must be moving. 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. Mungan, spring 2009 in this brief note i show that the quantum length, equal to the cube root of the quantum volume which in turn is the reciprocal of the quantum concentration, given by. In fact radiation shows dual nature sometimes as wave and sometimes as particle.
Fundamentals of quantum mechanics deriving the rayleighjeans radiation. By analogy with the wave and particle behaviour of light that had already been established experimentally, the french. The original davisson and germer experiment was an investigation of how electrons scattered after hitting different kinds of metallic surfaces. In 1905, einstein suggested that light has a dual character, and behaves both as a particle and a wave. Dual behaviour of matter debroglie equation according to this, matter like radiation posses dual behavior i. Thus, every object in motion has a wavelike character. Electron microscope is a common instrument illustrating this fact. Ncert chemistry class 11 unit 2 broglie relationship. So, both matter and radiation should have the similar properties. How slowly would a 4400 kg elephant have to walk in order to have a wavelength equivalent to visible light at 5. As i understand it, the derivation begins with two of einsteins equations. Matter waves are a central part of the theory of quantum mechanics, being an example of.