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. This means that photons, electrons possess both momentum as well as wavelength. Electron microscope is a common instrument illustrating this fact. By rearranging the momentum equation stated in the above section, we find a relationship between the wavelength. As i understand it, the derivation begins with two of einsteins equations. It means when the matter is moving it shows the wave properties like interference, diffraction etc. Pdf a charged photon and its lightspeed helical trajectory form a surprising new solution to the. The debroglie wavelength will be our primary physics input for the development of quantum mechanics. By analogy with the wave and particle behaviour of light that had already been established experimentally, the french. However, not all these explanations can be represented in mathematical form, or they do not provide a physical mechanism, justifying formula 1. How slowly would a 4400 kg elephant have to walk in order to have a wavelength equivalent to visible light at 5. Dual behaviour of matter debroglie equation according to this, matter like radiation posses dual behavior i. Very low mass particles moving at speed less than that of light behaves like a particle and wave. Matter waves are a central part of the theory of quantum mechanics, being an example of.
So, matter should have wave which can be expressed as. 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. His concept about the dual nature of matter was based on the following observations. The debroglie equations can be derived from the einsteins famous equation of energymass equivalence and planks theory of quantum radiation. The derivation of schrodingers equation is not straight forward. 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. What is the magnitude of the velocity of this electron.
For an object to have a wavelength, it must be moving. In fact radiation shows dual nature sometimes as wave and sometimes as particle. 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. According to debroglie hypothesis, the energy of the universe is in the form of matter and radiation. Thus, every object in motion has a wavelike character.
Equation 11 connects the module of the momentum p of a particle with the wavelength. In 1905, einstein suggested that light has a dual character, and behaves both as a particle and a wave. It seemed reasonable to wonder if electrons could also have a dual waveparticle nature. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. There must be a correct way of deriving it for electrons etc. Fundamentals of quantum mechanics deriving the rayleighjeans radiation. It basically describes the wave nature of the electron. But then, the wave nature of electromagnetic radiation is called into question when it is involved in blackbody radiation, photoelectric e. But in the end one cannot derive this relationship.