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I have been trying to understand "wave-particle duality" and other cases related to it. I am currently a college level student. I have few question which I am not getting answers clearly.

In double slit experiment, A particle behave like a wave, then how is "wave-particle duality" explained? I mean, If the particle behave like wave, then is it generating a wave or behaving as a wave? Is that wave going horizontally through slits(Double Slit Experiment) or vertically up and down or in which direction/axis the particle is vibrating to have a specific frequency? How does light behave as waves in it? and how does observer modify the experiment?

I may be thankful to you, If you clear my problems. I have read the theories on Wikipedia and other informational sites and tried to understand it.

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Short answer as I understand it [I have never really done a focused study on QM though!]: The wavefunction, whose magnitude can be viewed as the probability of finding a particle at that point, behaves like a wave and so can interfere with itself, even though any observation shows particles arriving as discrete quanta. I think it's dead wrong to say that it's generating the wave. The particle IS the wavefunction, because the particle behaves probabilistically. –  NeuroFuzzy Feb 14 '13 at 23:04
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4 Answers 4

The demonstration shown in the answer of another respondent, with the time frames showing how the interference patern builds up over time, is one of the best pieces of evidence we have about the wave particle duality of matter at the quantum scale. An intersting aspect in all these mysteries of nature, that I would like to express my opinion about, is the following:

Let us talk about photons, because they are the most missunderstood objects in quantum mechanics discussions.

Wave or particle? Photons are particles every day of the week, not some days they are waves and some other days they are particles. They are as much particles as the electrons are. We know that from the distinct clicks we hear in our detectors when sufficiently low intensity light arrives at them. The wave property of the photon, or any other particle, is the wave function, and I assume we are familiar with the interpretation given to it, as the probality to observe the photon (or any other particle) at some position $x$ at some time $t$. That is to say that there is no way to tell were actually the photon is before we observe it. The wave function in the mean time occupies the whole of the space that is available for the photon to be in. It is important to undestand that photons of the same colour are all identical (they have the same energy).

Two slit experiment: Now let us see what happens when a photon approches the two slits. The wave function that represents the photon will pass through the slits like waves do. It will split into two waves and recombine to interfere on the aray of detectors on the other side. The maxima corespond to high probability, the minima to zero probability. The consequence of this is that the photon is most like to show up in one of these maxima and will only hit one detector, but we don't know which one. Likewise, we don't know which slit it has gone through. An interesting point to make here is this, there is no way that one photon will hit two detectors at a time. Any attempt, or trick we might do to determine which slit the photon has gone through, destroys the interference pattern as all wave properties are removed!

Conclussion: The interference pattern people had seen in the Young experiment when they did it, they observed the pattern forming instantly because they used high intensity light. But we discover the reality when we use very low intensity light. It is like you turn down the water tap, and you start getting droplets instead of that continuous flow you had when the tap was fully open. And we know that if we look closer we will see molecules of water.

For a deep discusion on all these, try to google: Richard Feynman's lectures at the university of Auckland, New Zealand, First Lecture. Very entertaining too! Try this link: http://vega.org.uk/video/subseries/8

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This wikipedia article has a double slit experiment with individual electrons which really shows the particle/wave duality.

What one should keep clear in one's head is that

a) the particle nature is given by the ability to locate a "particle" at a specific (x,y,z,t) maybe with some delta errors.

b) the wave nature is found in the probability distributions of these particles, the probability of finding them at a specific (x,y,z,t)

The following experiment is accumulating electrons one by one .

electrons through  slits

*successive accumulation of electrons *

In the first exposures one does not see much of a pattern. When enough statistics is accumulated the interference pattern is seen in the probability distribution for these electrons.

An experiment in 1987 first determined the "particle" position and the wave nature simultaneously.

In this recent experiment the slit the photon passed through is ingeniously known, and it shows that the photon passes from a unique slit.

That the interference pattern appears to be destroyed when the slit the "particle" passed through is known, is because the older measurements destroyed the information by disturbing the path when trying to detect it.

"Particle" in quotes because in the microcosm world the only concept of a particle is a disturbance in the experimental apparatus, that can be described as a billiard ball is described macroscopically, by its position . What we have is a quantum mechanical entity that has an (x,y,z) location within the uncertainty principle, which (x,y,z) is given by the quantum mechanical probability function describing the dynamics of its path. It is a probability wave , not a "mass" wave, i.e. it is a bad visualization that the "particle" is distributed in the whole possible space . Just the probability of finding the "particle" depends on a wave function distribution which creates an interference wave pattern at detection.

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That ruins the hundreds of popular science explanations I've heard: that, "if we know which slit the particle goes through, it only goes through one and so can't interfere with itself". I can't find an article on this, could you link one? –  NeuroFuzzy Feb 14 '13 at 23:07
    
@NeuroFuzzy it clarifies whence the full "complementarity" widely assumed arouse. the measurement accuracies/methods . Here is another link more recent than the link in the wiki article livescience.com/… . It does not ruin quantum mechanics which works with probability distributions . Just a fuzzy concept of it in the popularization of science. –  anna v Feb 15 '13 at 5:59
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I'm studying qm too, so I'll try to answer it (but not really sure of what I'm saying) In the two slits experiment the two waves are supposed to be monochromatic (from the same source with a defined wavelength) and with the same polarization. The polarization of the wave tells you the direction of the wave vector. The light can have a circular polarization, but I think that this point it's not really important, the important thing it's they have the same polarization. So I think that the direction of oscillation doesn't affect the result.

The light behave like a wave because an interference pattern it's build up on the screen, that is identical to the pattern created by a real wave. The only difference is that the pattern of interference of a real wave it's time dependent (the band's width change in time) while the pattern due to light or electron beams are not time dependent ( the band's width doesn't change in time) but they are gradually built as the particles hit the screen. This it's because a real wave it's described by a real function, while the qm uses a complex function. When you try to find the intensity of the complex function you get rid of the time as you have to do the squared modulus, but not so if you do the same for a real superposition of the 2 wavefunctions from the two slits.

Experimentally, if you can figure how through which slit the particle passed by, the interference pattern is deleted. This have something to do with the nature of the problem, not with the method of the measurement I think. This is strictly related with Heisenberg principle of uncertainty and with the concept of wave packets (a sort of Fourier transformation is involved if you try to describe a particle having an uncertainty on its wavenumber).Anyway, this isn't clear for anyone I guess.

For a better explanation, try to read Introduction to Quantum Mechanics by Phillips. I'm reading it and it's not bad!

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I struggled with how to think about this very same issue.

The result of the double slit experiment showed that when a beam of photons ( or any particle for that matter ) is shot at two slits, the pattern on a screen placed at the other end will be that of alternating light and dark bands. A lot of mathematics in Physics works out very nicely when we look at particles as particles, so we assumed that this is what they are. If you were to place the slits in a tub of water such that they are half submerged and send a disturbance towards the slits, the two slits will act like two point sources of two more waves apart from the original. The result of these two water waves mixing peaks to troughs and the myriad of mixtures of amplitudes will be that same alternating light dark patter, but with water amplitudes ( alternating peaks and troughs ).

So because of the fact that particles are very well described as just particles, but exhibit wave like nature and can be described just as well with waves, particle-wave duality is born. As for the angle at which the waves go through the slits, I would go so far as to say that it is completely arbitrary, akin to unpolarized light.

As for the frequency: The Planck-Einstein Relation is what connects the wave and particle nature of a particle. It states that the Energy of a particle is equal to the frequency of the particle wave multiplied by Planck's constant. In symbols

$$ E=h\nu $$

Rearranging for the answer to the frequency of the particle in question gives you:

$$ \nu =E/h $$

Which is the frequency of the associated particle wave. If you know the Energy of a particle, you have the frequency of it's wave. The same is also true for light, and any other particle that we have observed thus far.

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