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Since a wavelength, $\lambda$, is the length of a entire cycle

picture showing a wavelength being measured from different points of a wave

How many $\lambda$ (complete cycles) can a composed wave have? I mean, for $n \lambda$, how big can $n$ be? And what does it mean, physically?

I'm not necessarily talking about an electromagnetic wave, it can be an 'electron wave' since particles can be interpreted as waves.

Iberis
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    Why do you think there is a limit? – Ghoster Feb 11 '24 at 18:23
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    Turn on a laser. Wait however long you want. – Jon Custer Feb 11 '24 at 18:26
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    This depends on the size of the universe. – my2cts Feb 11 '24 at 18:49
  • Theoritically n has no limit but physically n must be finite because no single infinite wave can not exist and you can only have wave packets – Sancol. Feb 11 '24 at 21:05
  • @JonCuster Speaking of an ideal theoretical laser, yes. – kkm -still wary of SE promises Feb 12 '24 at 02:22
  • The wave function modelling mathematically a particle wave gives predictions for the probability of finding a particle at an (x,y,z,t). To check the prediction one has to use a number of particles with the same boundary conditions. the answers to this question may help you , also my answer here https://physics.stackexchange.com/questions/100443/does-electron-in-wave-form-have-mass/100452#100452 – anna v Feb 12 '24 at 05:02

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The mathematical wave you are showing , has no limit of length it can go from minus infinity to plus infinity,

When a mathematical wave function is used to fit specific physical behavior, as waves of water and sound, it will depend on the particular boundary conditions of the case under study,and more than one function will be needed.

water wave

For the case of the laser, which has a fixed wavelength within error, the length it can travel will depend on the energy available before the wave turns into the photons that compose it, because all laser beams have a divergence with distance . Photons are not a wave, so that will be the end of the laser beam.

anna v
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A single photon would represent a "cycle", in a laser we have stimulated emission which means a single photon passes by an excited atom and induces another identical photon instantaneously.

Photons are always created one at a time by electrons in atoms .... and photons are always absorbed one at a time. In the laser cavity we have unique constant sinusoidal EM field ... you can think of photons jumping into this field ... this gives a lot of synchronicity to the emitted single photons.

A material wave can go on as long as you want.

PhysicsDave
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  • I'd be a little bit more careful about photons; perhaps saying that a light wave stimulates an emission of a phase-coherent wave by an excited atom, shedding an exact quantum of energy, like you explain at the start of the second paragraph. Reading this, I bump into the concept of the "phase of a photon", which, unlike wavelength-energy, is hard to make physical sense of. Light-as-particles is a tricky business when it comes to lasers or mirrors: coherent light's phase follows the normal wave equation, but the photon's contribution to the phase is, strictly, neither observable nor calculable… – kkm -still wary of SE promises Feb 12 '24 at 02:17