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You are wrong, what represents the probability is the square of the wave, which is always positive. There is still no agreement on the physical interpretation or the meaning of the wave itself, that is still an intense field of debate on the foundations of quantum mechanics.


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I like @Simon 's answer, but my personal favorite method to "derive" the Schrodinger equation is this. Think of the quantum state as encoding some information about your system. That is to say some quantum version of a probability distribution defined on a vector space (Hilbert space). What do we want of a meaningful probability distribution? First it ...


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In order to understand the Schrodinger equation, you must know what the state vector is http://en.wikipedia.org/wiki/Quantum_state. Before we mesuare the system, its state could be any linear combinations of eigenvectors. The probability of obesrved value is square of the coefficient (also called wavefunction) of the corresponding eigenvector. When state ...


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The main confusion comes from people not realizing that when one talks of wave particle duality the wave part belongs to the probability distribution which can be calculated using the quantum mechanical solutions for the problem at hand. The solutions are called wave functions because they have sinusoidal expressions which are characteristic of the ...


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As I'm sure that you are aware of, the explanation that you are looking for is currently missing. Today, a limited reasoning is handed to you, accompanied of course with mere mathematical equations used to replace an actual explanation. However, we can view what we understand at this time, and put these pieces together, thus at the same time not be ...


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Wave-particle duality is an old concept that doesn't have any meaningful explanation power. It's not how we approach quantum mechanics today. Truthfully, it's about as bad an idea to teach wave-particle duality, as it would be to introduce relativity with the detailed explanation of the ether, just to end that lesson with the phrase "and that's why the ether ...


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If you search this site for wave particle duality or something similar you'll find lots of questions addressing this and related issues. The most complete description of particles we have is that they are excitations in a quantum field - this is called quantum field theory. Under some circumstances these excitations can behave like particles and under other ...


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Unfortunately, in quantum mechanics "ordinary" reasoning does not get you anywhere. The photon, like any other particle, is neither a particle nor a wave; it is an entity that we can only describe mathematically. It's only when we observe it that it shows up as either particle or wave. Or senses, and hence our logic, evolved to make sense of the real ...


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What you think as a particle, the electron for example, is a quantum mechanical entity that behaves as a classical billiard ball in some experiments but collectively displays behaviors that cannot be explained by classical mechanics, one of them is to display a wave nature, i.e. interference phenomena, when studied appropriately. I will repeat some ...


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An experiment which should be able to be easy to perform by someone with access to a lab is to place two double slit experiments side by side. Have a BBO crystal create a downconverted photon pair and have each of the pair interact with their own double slit experiment. Close the outer exits to both double slit experiments. If both photons exit the inside ...


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The particle/wave duality is an old concept that has never done anything good for anyone (not even Einstein and de Broglie). It's time to let go of it, even among the "groupies". We know "how" quantum mechanics works and the answer is "neither". What you are basically asking is for an experiment that can decide between two outright wrong models. Obviously, ...


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Tadeas Bilkas answer let me think about the sence of all and all time citing the quantum mechanics. I write his answer in terms of common mechanics and get the same result: You have an emitter of balls which radiates just one single ball but in a spherical area. You place a lot of baskets some meters apart (with same distance) from the emitter. Mathematics ...


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In case you "run out of photons", you must switch to probabilistic description of quantum mechanics. Let's consider an extreme case: You have an emitter of spherical waves which radiates just one single photon. You place a lot of detectors some meters apart (with same distance) from the emitter. QM says that the photon propagates as a probabilistic wave to ...


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The classical electromagnetic field given mathematically by Maxwell's equations can be proven to emerge from a confluence of individual photons, which photons are described by the Quantum Mechanical form of Maxwell's equations. Thus the classical wave is made up by zillions of photons with energy $h\nu$, where $\nu$ is the frequency of the classical wave. ...


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"Running out" of photons simply means that your wavefront is absorbed or scattered in a different direction or something like that. Either way, the original wave is "consumed", so you loose intensity or photons, depending on which picture you like better. For the case of a single photon source: One photon can only interact with one electron. However, there ...



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