in classical physics frequency represents how many cycles in one unit time, but I do not know how we define a frequency for a particle? what does it mean for a particle to have a frequency, the book I read it from just says Energy is proportional to the frequency of the photon but where is frequency?
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Two ways to think about this: instead of thinking of one photon, think of the Quantized Electromagnetic Field. This quantum field is spread throughout all space and time and is everything electromagnetic. An elementary way to think about it is as a collection of quantum harmonic oscillators, one for each of the classical modes of Maxwell's equations.
If you have studied the quantum harmonic oscillator, you'll know it has associated with it a frequency. This frequency can even be classically measured if it's quantum state is, for example, a coherent state with a big enough displacement from the ground state.
So we have our quantised electromagnetic field, and it, intuitively, comprises little "energy bins" (the quantum harmonic oscillators), each labelled with a different frequency, and each with the potential to have its unique frequency label measured classically if it is in the right state.
A photon is now a lone, energy quantum added to one of these oscillators. These oscillators communicate with the outside world, discretely, through fixed sized energy quantums, in interactions. It is these interactions we see when we measure electromagnetic phenomenons. So in this point of view, the photon's frequency is not so much a frequency of the photon considered alone, but the frequency of the quantum harmonic oscillator it is added to / withdrawn from.
Another way to look at this is as a frequency of a probability wave. Marvn Scully and M. Suhail Zubiary in their book "Quantum Optics" show that the probability density to find a photon (i.e. detect it destructively with e.g. a photomultiplier tube) when the electromagetic field is in a one photon state is the squared magnitude of a vector quantity that is a solution to Maxwell's equations. This solution can also have a frequency associated with it, just like any other solution to Maxwell's equations.
Selene Routley
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a particle can be described by a wave-function. The frequency of the wave is given by the de Broglie relationship
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I know it , but im asking about the meaning , the definition of frequency to a particle in the sense of E=HF introduced by Einstein – Mohamed Osama Dec 07 '14 at 22:16
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you can consider it as it's only a spatial variation in the phase – Mohamed IBrahim Dec 07 '14 at 22:18
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Sorry , can you elaborate more? – Mohamed Osama Dec 07 '14 at 22:19
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try to see answers to this question http://physics.stackexchange.com/questions/108471/how-does-the-frequency-of-a-particle-manifest-itself – Mohamed IBrahim Dec 07 '14 at 22:24
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There are a few ways to think about, the worst being trying to imagine a particle as a solid little ball behaving in some oscillatory way.
Particle are described by quantum field theory. So for a particle, say an electron, there is a corresponding quantum field (electron matter field in this case). The particle of the field is an excited mode of the field, so you can think of a particle as a wave in this field. Depending on your knowledge of waves it might be difficult to understand how this wave is localized into something point like.
So maybe the best way to think about it is by experiment. Consider a wave incident on an obstacle in proportion to its wavelength, such as a diffraction grating. Behind the grating the waves interfere an produce a diffraction pattern. Particles, suitably prepared, will produce interference patterns and from these patterns the particle's wave properties can be inferred.
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There are several ways to measure the frequency of a photon.
The most direct way is to "mix" the photon beam with another of a precisely known, slightly different frequency. This produces signals whose frequencies are the sum and difference of the 2 beams. If your mixing frequency is well chose, the difference will be low enough to be directly countable in electronic counters. This system is used in radar speed cameras.
You can measure the frequency of a wave by letting it interfere. Shine the photons through 2 narrow slits, and observe the pattern of light and dark areas on a detector behind the slits. You can compute the frequency from the pattern and the geometry of the slits. This page shows how Thomas Young first computed the frequency (actually, the wavelength) in 1803. To convert wavelength to frequency, the only other thing you need is the speed of the wave. This works with any other particle (electron, proton, etc) that behaves like a wave.
More general information can be found here
hdhondt
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