If elementary particles are represented as oscillations of their respective fields, why are atomic orbitals said to represent the probability of finding an electron at a specific location in the electron cloud or orbitals like it is a solid particle? Isn’t it more plausible or intuitive to think of the atomic orbitals (wave functions, oscillations) as the actual particles (electrons) themselves? Like for example the way a single hydrogen atom is experimentally imaged here (specifically page 13, fig.3, if you don’t want to look through the whole article):


Why are the results described as probability distributions in the above article? Or the way electrons are imaged here as something that looks like typical normal modes of oscillation (specifically last four pages of the first article and last page fig.4 in the second one):



I understand that for example in the last two articles the images show the momentum distribution of the electrons, but wouldn't that distribution correlate to actual fluctuations of the substance of whatever the electron field would consist of?

Or if I have a totally wrong understanding please correct me.

  • $\begingroup$ Atomic orbitals are a construct featured in quantum theories of particles, not in quantum field theory. The electrons are seen as point particles for that purpose. The predictions of quantum field theory should reproduce the predictions of single particle quantum mechanics in an appropriate limit. I do not know a precise treatement of this limit in the case of relativistic QFT. $\endgroup$ – Adomas Baliuka May 28 '17 at 19:21
  • $\begingroup$ If everything at the deepest level is made of little vibrating oscillations of fields (which sounds like a very logical and intuitive notion) what is the essence of these oscillations? Why do particles keep coming back to the picture? I mean of course the oscillations could be viewed as point particles, compared to macro scales, but not as solid particles. $\endgroup$ – Georgi Pavlov May 29 '17 at 18:34
  • $\begingroup$ When we combine Quantum Mechanical concepts with Field Concepts we get Quantum Field Theory. $\endgroup$ – Georgi Pavlov May 29 '17 at 18:34
  • $\begingroup$ a number of relevant questions and answers on physics.se come up if you google "wave packets in QFT" $\endgroup$ – anna v May 30 '17 at 3:38

At energy scales sufficient for the creation or destruction of particle-antiparticle pairs, we have to talk in terms of fields. At low energies, we can talk in terms of $N$-particle states because $N$ cannot change. Then wavefunctions can describe these states, e.g. Slater determinants can describe systems of identical fermions. Orbitals describe individual electrons' probability distributions in such fixed-$N$ systems. This is what we expect in atomic physics.

  • $\begingroup$ @GeorgiPavlov Empirical particles and waves and their duality are recovered in a suitable limit from field theory. Particles have therefore been described as "bumps on a field". $\endgroup$ – J.G. May 28 '17 at 20:10
  • $\begingroup$ So in reality a "solid particle" would be an abstract term while a localized transverse spherical standing wave (oscillation) would be a way better and real (accurate) representation of a "particle" and not the other way around. $\endgroup$ – Georgi Pavlov May 28 '17 at 20:11
  • $\begingroup$ I have only a basic understanding of concepts of QFT, because of the very short time I've been exposed to it, but I've always found mathematics really pleasant, so I gradually grasp its concepts more and more. Like Slater Determimants, applied to Wave Functions at the context of Atomic Orbitals. But on a basic physical picture, how can a field (some form of a 'fluid'-like substance) have bumps in it? What would be the essence of the bumps? It can have waves. Waves and bumps would be synonymous, also in the mentioned application at the mentioned context. $\endgroup$ – Georgi Pavlov May 28 '17 at 20:30
  • $\begingroup$ @GeorgiPavlov You'll understand these issues better if you study the integral representation of free fields, where you'll see wavelike coefficients of ladder operators, including creation operators that promote the vacuum to a $1$-particle state. $\endgroup$ – J.G. May 28 '17 at 20:32
  • $\begingroup$ I know about the mathematical formulation of creation and annihilation operators (again of course basic concepts) of course, as they are some of the most basic aspects of QFT. But they do not describe a 'solidification' of the field. Rather rippling or vibrating of the field, which creates certain normal modes. $\endgroup$ – Georgi Pavlov May 29 '17 at 5:58

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