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What are the experiments performed to determine the position of an electron inside the atom to verify the probability wave function data? Is it possible to do those experiments in real life?

Qmechanic
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Moonzarin Esha
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    This is a great question. In fact, wave functions were being manipulated even before they were understood as representing a probability amplitude. – Paul Young Jan 13 '19 at 19:20
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    Possible duplicate: Can we measure “wavefunction” of quantum particles? – Chiral Anomaly Jan 13 '19 at 20:05
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    And a possibly-relevant paper: "Tomographic imaging of molecular orbitals" (2004), http://xrm.phys.northwestern.edu/research/pdf_papers/2004/itatani_nature_2004.pdf. The abstract says, "Here we demonstrate that the full three-dimensional structure of a single orbital can be imaged..." For an intro, the website https://www.iqst.ca/quantech/qtomo.php says: "Quantum tomography is the art of determining a quantum state from making measurements on multiple copies of the state with multiple modifications of the measurement apparatus." – Chiral Anomaly Jan 13 '19 at 20:06
  • https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.110.213001 (with some discussion of it at https://futurism.com/the-first-image-of-an-atoms-wave-function-2) – BowlOfRed Jan 14 '19 at 01:43
  • Where you say "verify the probability wave function data? " do you mean "verify the wave function theory"? – DanielSank Jan 14 '19 at 02:45
  • Please note that it's not nice to make edits which invalidate existing answers. There has been a meta discussion regarding some edits made here. It's better to ask a new question under such circumstances. Usually, the offending edits will be rolled back, but in this case, there are answers which address the new question. –  Jan 14 '19 at 08:43
  • @dan-yand could you please tell me how the position of a single electron is found out thereby constructing those orbitals? – Moonzarin Esha Jan 15 '19 at 15:25

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Hyperfine interactions allow probing the wave function at the position of the nucleus, especially the contact density and the spin polarization of $s$ orbitals. It is a large field with several spectroscopic methods. The interaction influences both the electron energy and nuclear levels. The Mößbauer effect is especially striking. Using the Doppler effect, one can measure minute changes in the energy of nuclear transitions. The isotope Fe-57 (daughter of radioactive cobalt-57) has a very suitable transition at 14.4 keV. With the Doppler effect one can measure spectra with many lines that give information about oxidation state and magnetic moment of the atom.

The total shape of the orbitals can be measured by x-ray diffraction, which can be used to generate electron density maps of crystalline substances. Neutron diffraction can measure spin densities.

Photoemission spectroscopy is used to measure energy distribution functions which can be compared with theoretically computed densities of states.

With positron annihilation one can measure momentum distributions.

  • @Pieter Could you please tell me how the position of a single electron is found out thereby constructing those orbitals? How are those hyperfine interactions close to the nucleus are done? – Moonzarin Esha Jan 15 '19 at 15:33
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Clear examples of the spatial probability distributions come from X-ray crystallography. This technique is widely used for determining the atomic and molecular structure of crystals.

An incident X-ray beam is diffracted by a crystal into many specific directions. The X-ray diffraction pattern can be calculated back to the electron probability distribution.

X-ray Crystallography Platform
Picture taken from X-ray Crystallography Platform of www.creative-biostructure.com

Thomas Fritsch
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  • Could you please tell me how the position of a single electron is found out thereby constructing those orbitals? – Moonzarin Esha Jan 15 '19 at 15:39
  • @MoonzarinEsha AFAIK with this technique you cannot examine a single electron. You can only determine the total probability density map of all electrons. – Thomas Fritsch Jan 15 '19 at 16:39
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Edit after change of title and content one hour after I answered the question, making a drastic change by inserting "inside an atom" in the title and the body

Original title to which the following is an answer:

What are the experiments performed to determine the position of an electron to verify the probability wave function data?

The clearest example of the probability distribution in space comes from the experiment: "electron of specific energy scattering off two slits of specific width and distance"

dblslit

electron build up over time

One needs to do the experiment with the same boundary conditions for the electron accumulating events, the footprint of each electron on the screen. In the top frames it looks random, but slowly the interference seen demonstrates the wave function solution for the specific probability distribution.

A huge number of experiments accumulating probability distributions exist, the latest gave us the discovery of the Higgs.

anna v
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  • @anna v, sorry for the late edit,I understand how this double slit electron experiment can be performed but Could you please tell me how the position of a single electron is found out thereby constructing those orbitals? – Moonzarin Esha Jan 15 '19 at 15:37
  • In my answer there are no orbitals, because I gave the simplest status of measured probability distributions.. Here is an explanation with words, https://physicsworld.com/a/quantum-microscope-peers-into-the-hydrogen-atom/ but to really understand the experiments you have to study the mathematics behind it. It is similar to how from xray patterns of crystals one can reproduce the crystal structure using transrorms. https://en.wikipedia.org/wiki/X-ray_crystallography – anna v Jan 15 '19 at 15:42