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It's said in textbooks that electrons won't radiate and fall into nucleus because matter wave of it's form a standing wave but could somebody explain why being a standing wave it doesn't radiate, even standing wave oscillates at a particular position and hence have acceleration and hence it should radiate right but it doesn't happen. could some one explain this . I understand that being standing wave it shouldn't lose energy so that it won't change it's wave property but at the same time it's said that it accelerates over time but acceleration means radiation should happen but it doesn't so what prevents it from radiation

JSJ2004
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    possible duplicates https://physics.stackexchange.com/q/20003/291677 and https://physics.stackexchange.com/q/278680/291677 – Quantum Mechanic May 17 '22 at 17:09
  • @QuantumMechanic I do not see a duplicate. The previous posts you have cited were referring to the classical model. The present question is completely different. It is completely inside a wave model for electrons. I will propose reopening it. – GiorgioP-DoomsdayClockIsAt-90 May 18 '22 at 07:47
  • Yes, I agree with Giorgio. – John Rennie May 18 '22 at 10:34
  • @GiorgioP I only said possible, there are quite a few questions of this ilk floating around on the site that could help OP: also https://physics.stackexchange.com/q/88441/291677 and https://physics.stackexchange.com/q/44949/291677. The questions are all a bit different but the answers must all be the same: we make up a new rule for electrons to obey, call it the Schrödinger equation, then consider the implications – Quantum Mechanic May 18 '22 at 20:26
  • also https://mathoverflow.net/q/119495 – Quantum Mechanic May 18 '22 at 20:30
  • @QuantumMechanic All the links, including the last ones you cited, are connected to the stability of the atoms. However, almost every question is about a different issue connected to stability. In particular, I do not see other questions addressing the same issue underlying the present one. – GiorgioP-DoomsdayClockIsAt-90 May 18 '22 at 21:19

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The standing wave idea doesn't help us with acceleration; as realized by OP, standing waves do indeed have their constituent parts accelerate over time. The idea is that standing waves do not decay: they do not lose energy, they do not change their wave properties over time, they always return to the same initial position, etc. If any part of the wave got lost (if the electron "begins" to radiate), the boundary conditions will no longer hold and we will no longer have a standing wave.

Note that this answer is circular! We just posit that standing waves don't change over time, then use this to explain why electrons don't change over time. This was part of the early quantum theory (https://en.wikipedia.org/wiki/Old_quantum_theory) and was superceded by the Schrödinger equation for explaining where the quantized energy levels come from and why only certain orbits for electrons are allowed.

Quantum Mechanic
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  • I understood being standing wave it shouldn't lose energy so that it won't change it's wave property but at the same time it's said that it accelerates over time but acceleration means radiation should happen but it doesn't so what prevents it from radiation – JSJ2004 May 18 '22 at 05:19
  • @JSJ2004 by energy conservation, if an electron radiates energy, the electron must lose energy. According to quantum theory, the electron can only change energy by specific [quantized] amounts and there is a lowest-energy state: that directly prevents a continuous radiation over time – Quantum Mechanic May 18 '22 at 20:28
  • So if it doesn't radiate as energy is quantized so what happens to electric and magnetic fields created by it or will any of these component won't be there – JSJ2004 May 19 '22 at 03:34
  • @JSJ2004 there won't be any electric or magnetic fields that corresponding to radiation (ie, to traveling modes that carry away energy). There will still be the fields corresponding to the electron and proton's Coulomb interactions, which technically means there will be virtual photons mediating this interaction that do not radiate energy away from the electron/proton – Quantum Mechanic May 19 '22 at 21:09
  • Could you please explain what are virtual photons . Also you said it won't carry energy so what prevents magnetic and electric field to store energy – JSJ2004 May 20 '22 at 08:39
  • @JSJ2004 virtual photons get created in pairs in the presence of electrons and protons but then annihilate with each other or something else before carrying energy out to infinitely far away. The magnetic and electric fields can store energy, it's just that they won't carry this energy off to infinitely far away (ie, they won't correspond to radiation) – Quantum Mechanic May 20 '22 at 18:24
  • If magnetic/electric field is created it should induce other and this chain continues and radiation should take place but you told it won't so what prevents these to induce each other. Also one more doubt how an extra proton and electron created for forming virtual photon and can a proton cancel electron(I know only very basics, to my knowledge e- + p+ +antineutrino = neutron) – JSJ2004 May 21 '22 at 01:11
  • @JSJ2004 not all magnetic and electric fields correspond to radiation that carries energy to infinity. The antiparticle questions are really a whole new set of questions belonging and I have to recommend learning some introductory quantum field theory for them: we don't have electrons and protons annihilating each other in this case, we just have photons being created and annihilated – Quantum Mechanic May 22 '22 at 13:24
  • I understood not all electric and magnetic fiels cant form radiation but what prevents them from doing so and also one more thing what you mean by two particles annihalating is photon and antiparticle of photon if yes is there any special condition that make a magnetic and electric field produce antiphoton along with normal photon – JSJ2004 May 22 '22 at 15:57