For the love of physics walter lewin may 16, 2011 duration. If the velocity of the electron in this microscope is 1. The wavelength has an inverse dependence on velocity and becomes infinite in the particles own reference frame. Although he originally wanted a career as a humanist and even received his first degree in history, he later turned his attention to physics and mathematics. If e is the kinetic energy of the material particle of mass m moving with velocity v,then. Difference between phase velocity and group velocity. Two fundamental equations regarding waveparticle duality are. Phase velocity is the speed of the crests of the wave. If we superpose matter waves to form a wavepacket that represents the particle, the packet will move with the so called group velocity v. But then, the wave nature of electromagnetic radiation is called into question when it is involved in blackbody radiation, photoelectric e ect and such. It seemed reasonable to wonder if electrons could also have a dual waveparticle nature. So, the phase velocity equals to the group velocity. And yes, not only does a particle need to be moving to produce wave effects, it needs to be moving at a velocity faster than a certain threshold.
The phase velocity wave velocity of a wave is the velocity with which any given phase of the wave travels. For example, the phase velocity is equal to the group velocity when sound waves travel through the air as air is a non dispersive medium for sound waves. 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. The particle velocity should be always equal the group velocity of the corresponding wave. Quantum physics i, lecture note 4 mit opencourseware. Group velocity the group velocity of any particle massive or massless is equal to the derivative of its total relativistic energy with respect to its relativistic momentum. Beiser calls it v p, and later shows that vp is the phase velocity of the waves. We can show that the phase velocity is greater than the speed of light by starting with the equation relating energy to momentum and rest mass. Comptons formula established that an electromagnetic wave can behave like a particle of light when interacting with matter.
Determine the kinetic energy in electron volts required for electrons to resolve a large organic molecule. In non dispersive mediums, the phase velocity of waves does not depend on the wavelength. The theory of matter waves was used to justify quantization of. He sensed deeply the symmetry in nature and argued that if light sometimes behaves like a wave and sometimes like a particle, then perhaps those things i. And how we connect this with special relativity where the velocity depends on the frame of reference. Are these two equations independent or can one derive one from the other. In his 1924 phd thesis, he postulated the wave nature of electrons and suggested that all matter has wave properties.
The wavelength of a photon is calculated by combining einsteins equation for determining a. We assume that the wave packet or group is formed due to combination of the two waves having equal amplitude and different their angular frequency by dw and wave velocity dk. The wave is conceived as a kind of eld that guides the. For particles whose energy is not very high hmv, where m is the particles mass and v is its velocity. But then, the electron at rest will have infinite wavelength, and infinite wave phase velocity. In all his preceding works, the treatment frequency.
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