# Matter Waves Interference

When an EM wave diffracts, I can imagine that its EM field interacts with the charges in a certain obstacle thus inducing a wave behaviour on the charges of the matter that will interact with the EM of the photon.

However, I am having difficulty to make the analogy with matter waves. Since a matter wave is a result of a momentum, which implies kinetic energy, how does a matter wave is created in order to interfere with an electron with, for instance, 200 keV?

Since a single electron can be diffracted, this means that its wave must interfere with other induced matter waves, right? But wouldn't that imply the creation of high kinetic energy particles?

## 1 Answer

The confusion comes because you are thinking of probability waves, which is what the interference pattern from elementary particles through the double slit experiment are, as if they are classical waves.

Current day physics accepts that the fundamental framework of nature is quantum mechanical. Classical mechanics, classical electromagnetism are emergent theories from the quantum mechanical foundations, in an analogous way that thermodynamics is an emergent theory on the substratum of statistical mechanics.

The electromagnetic wave is a special case because the classical wave as given by Maxwell's equations emerges from the coherent synergy of a huge number of photons, i.e. elementary particles. If one is theoretically inclined here is a link which explains how photons build up the electromagnetic wave.

The photon's energy is given as E=h*nu where h is Planck's constant and nu the same frequency that manifests in the emergent from zillions of photons classical wave. The double slit interference appears even for a single photon at a time, and the pattern gives a probability distribution, the probability of finding the photon at an (x.y) on the screen.

The same is true for single electron interference patterns. It is the probability which is given by the square of the quantum mechanical wavefunction that manifests in the pattern. The electrons pass one at a time and are deflected according to that probability. There is no matter or energy wave in the quantum mechanical framework. Just a probability of detection.

• Thank you anna but I'm not sure I understand. If an electron doesn't suffer diffraction, we cannot create a pattern that is a consequence of the probability of detection. What makes the electrons to be deflected in the diffraction process? This sentence was a bit of a surprise to me "There is no matter or energy wave in the quantum mechanical framework. Just a probability of detection." I cannot express the doubts and lack of understanding that this brings to me :) – cinico Dec 4 '13 at 18:56
• Quantum mechanics is a mathematical formulation that fits all the data of the microcosm we know now . It simplest form is the shroedinger equation whose solutions, instead of giving, for example, orbits for the electron around the nucleus, give orbitals. en.wikipedia.org/wiki/Atomic_orbital . It is the square of the wavefunction that gives a probability of finding the electron in a specific (x,y,z,t). There are no trajectories as in classical orbits for example a satellite around the earth. – anna v Dec 4 '13 at 20:18
• Each electron in the two slit experiment follows the solution of a more complicated quantum mechanical equation that depends on the boundary conditions ( distance of slits etc) and again it will not be a specific trajectory but a probability distribution. It is the boundary conditions that determine the deflection, but the electron is whole when seen on the screen. There are even some experiments that have detected which slit the electron went through without completely destroying the interference pattern:en.wikipedia.org/wiki/… – anna v Dec 4 '13 at 20:24
• I should add that the name "wavefunction" comes because the QM equations are wave equations, i.e. have sines and cosines in their solutions. The interpretation of the square of the wavefunction as probability of detection has been tested over and over again and is basic in the description of the microcosm. – anna v Dec 4 '13 at 20:34
• Things are beginning to be a little more clear, but please consider the first half of your second comment: will we change the wavefunction of an electron by putting it into a system? Is the way that the system interferes with the original wavefunction described by an "operator"? Can the electron be described by a similar or completely different wavefunction after moving away from the slit? – cinico Dec 4 '13 at 21:03