The goto answer to that question is that the electron is a pointlike particle and cannot spin. The electron is not pointlike though. It is described by a wavefunction. One can prepare the wavefunction to describe a very small electron, but not a point-like electron. Is there a genuine answer to the problem?
3495
I often hear about subatomic particles having a property called "spin" but also that it doesn't actually relate to spinning about an axis like you would think. Which particles have spin? What does spin mean if not an actual spinning motion?
54680
I have a question about an argument used in Schwabl's "Advanced Quantum Mechanics" concerning the properties of the Klein-Gordan-Equation (see page 120):    Since the eigenenergies of free solutions are $E= \pm \sqrt{p^2c^2+m^2c^4}$the energy states aren't bounded from below. But I don't understand why that  then K-G-equation provide a scalar theory that does not contain spin and then could only describe particles with zero spin.   Intuitively, I guess because that spin can't regard by a scalar equation but I find this "argument" too squishy and would like to know a more plausible argument.
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Rather predictably, I'm having a hard time understanding quantum spin. I know that it has units of angular momentum and relates to rotation, but that it can't be thought of as the actual spin of a particle with real size. Also, I understand that it's quantized.  What I'm wondering is, what happens to quantum spin in a rotating frame of reference?  Specifically, are there (rotating) frames of reference in which (for instance) an electron has spin that isn't half-integer? Is there a frame of reference rotating about a single electron such that that one electron acts like a spin-0 particle?
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In an hydrogen-like atoms the orbitals are solutions to the Schrodinger equation suitable for the problem.  They describe the regions where an electron can be found.  So, why don't they have spherical symmetric?  As in this picture:    Why, in a certain distance from the nucleus, are there points where an electron can be found, and points where it can't?  EDIT: Is there any intuation about the symmetry breaking?
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It's an old-new question (I found only one similar question with unsatisfactory (for me) answer: )  It's strange for me how all books simply pass by such an important question, and mentioning strange and mathematically unsupported reasons such as:   orbits are stationary (while as I know this is just idealization, there is no stationary orbits in reality even for Hydrogen)  electrons are actually not localized due to uncertainty principle, thus they have no acceleration (while obviously in a non-spherically symmetric orbits a kind of "charge acceleration distribution" always exist) vacuum fluctuations play a major role (according to QED).   I'm not interested in how Bohr or Schroedinger explained it, I want to see a rigorous proof with QM, QED or maybe even the standard model as whole. I would like to see how this question was closed.
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This may seem like a slightly trite question, but it is one that has long intrigued me.  Since I formally learned classical (Newtonian) mechanics, it has often struck me that angular momentum (and generally rotational dynamics) can be fully derived from normal (linear) momentum and dynamics. Simply by considering circular motion of a point mass and introducing new quantities, it seems one can describe and explain angular momentum fully without any new postulates. In this sense, I am lead to believe only ordinary momentum and dynamics are fundamental to mechanics, with rotational stuff effectively being a corollary.  Then at a later point I learned quantum mechanics. Alright, so orbital angular momentum does not really disturb my picture of the origin/fundamentality, but when we consider the concept of spin, this introduces a problem in this proposed (philosophical) understanding. Spin is apparently intrinsic angular momentum; that is, it applies to a point particle. Something can possess angular momentum that is not actually moving/rotating - a concept that does not exist in classical mechanics! Does this imply that angular momentum is in fact a fundamental quantity, intrinsic to the universe in some sense?  It somewhat bothers me that that fundamental particles such as electrons and quarks can possess their own angular momentum (spin), when otherwise angular momentum/rotational dynamics would fall out quite naturally from normal (linear) mechanics. There are of course some fringe theories that propose that even these so-called fundamental particles are composite, but at the moment physicists widely accept the concept of intrinsic angular momentum. In any case, can this dilemma be resolved, or do we simply have to extend our framework of fundamental quantities?
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Why do we call a 1/2 spin particle satisfying the Dirac equation a , and not a  or a ?
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In  article it says:     The electrons can only orbit stably, without radiating, in certain orbits (called by Bohr the "stationary orbits") at a certain discrete set of distances from the nucleus. These orbits are associated with definite energies and are also called energy shells or energy levels. In these orbits, the electron's acceleration does not result in radiation and energy loss as required by classical electromagnetics. The Bohr model of an atom was based upon Planck's quantum theory of radiation.   My question is: how can this be if it is actually impossible? Any accelerating point charge should emit radiation, as explained , for example. It is not like I can posit the existence of an orbit where the electron is stable, just out of mid air. What am I missing here?
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I am a beginner in QED and QFT.  What is known (or expected to be) about bound states in QED? As far as I understand, in non-relativistic QM electron and positron can form a bound state. Should it be true in QED? Most of the basic text books on QFT I known treat QED with perturbative methods which do not help to study bound states. Is there a literature to read about it?  UPDATE: According to , electron and positron form a positronium. It is an unstable particle which can annihilate to two photons. In particular electron and positron cannot form a bound state. But still there is a logical possibility that several electrons and positrons can form a bound state (though probably once one has at least one electron and one positron, they will necessarily annihilate. Is it true?)  On the other hand, if one considers QED with both electrons and muons, then electron and antimuon form muonium. Clearly they cannot annihilate to photons. However in  in wikipedia it is claimed that muonium is unstable. Is it due to some effects of QED or due to actual presence of other, say weak, interactions?
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When we first discovered the proton and neutron, I'm sure scientists didn't think that it was made up of quark arrangements, but then we figured they could be and experiments proved that they were.  So, what is it about the electron that leads us to believe that it isn't a composite particle? What evidence do we have to suggest that it it isn't?
16822
In section 134 of Vol. 3 (Quantum Mechanics), Landau and Lifshitz make the energy complex in order to describe a particle that can decay:  $$ E = E_0 - \frac{1}{2}i \Gamma. $$  The propagator $U(t) = \exp(-i H t)$ then makes the wavefunction die exponentially with time.  But also, $H$ is non-Hermitian.  My question: Do we have to modify the basic postulates of quantum mechanics (as described by Shankar, say, or the earlier sections of Landau &amp; Lifshitz) to describe unstable particles?
57083
I'm tutoring senior high school students. So far I've explained them the concepts of atomic structure (Bohr's model &amp; Quantum mechanical model) very clearly. Now the next topic to be taught is semiconductors.  I myself am not conviced with the concept of electron holes. If there is no electron then there is no electron. How can it be a hole. We define a hole when there is some thing every where except at a place. But inside an atom how can we define a HOLE.  Kindly explain it with the help of Bohr's model. What was the need of introducing such abstract concept in semi conductors?
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Can two electrons be in the same state, when they belong to two different atoms, which are "far enough" (whatever that means) apart from each other?  With "same state" I mean that (as far as specifiable) the states are really identical, except for the position of the electrons.  More specifically: I am still not clear of how the separation of particles is taken into account for the Pauli exclusion principle. E.g. in a crystal the electrons seem close enough for the exclusion principle to become meaningful, for particles "a universe apart" from each other, it seems that it is kind of redundant (is there specific maths to that?), but what about everything in between?   (This is closely related to the talk Brian Cox gave, see this question: physics.stackexchange.com/q/18527/16689 )
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It is well established that:   'In quantum mechanics, the behavior of an electron in an atom is described by an orbital, which is a probability distribution rather than an orbit.   There are also many graphs describing this fact: : (hydrogen atomic orbital - one electron) In the figure, the shading indicates the relative probability to "find" the electron, having the energy corresponding to the given quantum numbers, at that point.  My question is: How do these symmetries shown in the above article occur?                 What about the 'preferable' axis of symmetries? Why these?
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In a normal atom, there is a limit of 2 electrons per obital due to the Pauli-Exclusion principle. I have seen people talking about replacing an electron with a muon, but since muons and electrons are distinguishable, would this then allow 2 electrons and 2 muons to occupy the same orbital, or would only 2 leptons be allowed to have the same set of quantum numbers?  For example, would a Beryllium atom with 2 muons and 2 electrons use only the 1S orbital, or would the 2S be used as well? Spectroscopic methods should be able to distinguish between the two.
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If I understand correctly, spin is an intrinsic property of particles, which follows the algebra of angular momentum, but has nothing to do with an "orbital angular momentum" in that the particle is not like a small sphere that rotates on itself, to which we could attribute an angular momentum as usual in classical mechanics, cf.  and  Phys.SE posts.   My question is: why does spin combine with orbital angular momentum to give total angular momentum? To me this is surprising, as spin, in fact, has nothing to do with a classical angular momentum. Any insight on that?
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Yesterday I asked this  concerning the existence of terms. This question is on the same topic. I have been looking at some tables (in Yang and Hamilton (2010), pg 199) at the terms that exist for two electrons in the same configuration. I noticed that for example if the state $^1S$ exists the state $^3S$ would not and vice versa. Is this a general rule? I.e. can we say:     For two electrons in the configuration $nl^2$ if the term $^1L$ exists then the term $^3L$ will not and vice versa.   If so can it be proved easily and if not why not?