Suppose a suitable energy is given to an electron in a shell, it will absorb energy and it jumps to the next orbit. Since it was highly unstable there, it will emit the energy as em radiation and comes to its original shell. For this to and fro jumping from one orbit to another, is the electron in need of any kind of acceleration?
f=ma --------[i]
Also
f=Eq ------[ii]
From [i] and [ii]
a=qE/m=((1.602 x 10^-19) x (257))/(9.1x 10^-31)
(as one Coulomb will experience a force of 257 Newtons)
=4.52 x 10^13 m/s^2
Electron will experience relativistic effects.
The question doesn't make sense, was addressed by Bohr and the answer is in all books on quantum mechanics. The electron is not in any unstable state, if it's in an eigenstate of the Hamiltonian-it evolves by picking up a phase.
Now, if you add to the Coulomb potential of the electron the potential energy of an external field, that, precisely, induces transitions between one eigenstate of the unperturbed Hamiltonian and another, you can ask what's the expectation value of the acceleration of the electron, in a given state (with respect to the total Hamiltonian)-as well as its probability distribution. That is a well-defined problem and has an answer that can be calculated with the formalism of quantum mechanics-similarly as for any other observable.
(as one Coulomb will experience a force of 257 Newtons) - Where does this come from?
The problem with QM is the lack of time dependance. It gives you answers but no understanding of processes. Maybe there is no possible description of the process. However, all you really need are answers and maybe we have just fooled ourselves thinking that we understand classical views of mechanics.
Of course quantum mechanics describes time dependence-through the probability distribution of operators in states, deduced through their correlation functions. Standard material in a course on (``advanced'') quantum mechanics, or (introductory) quantum field theory.
If my worthy RG colleagues find me wrong, I have no hesitation in admitting.
But, pls let me explain my point:
I equated the two forces[ rightly or wrongly] with the assumption that the electron is under a constant electric field of magnitude[say] 257 N/C.
Thank you for your answers.But we still uses classical Maxwell definition for the propagation of EM radiation in the space.Is there any QM definition for EM propagation in space?
Of course, in terms of photons-and it is known how to include their contribution-one effect of which is the Lamb shift. However the question discussed here implies that the electromagnetic field is classical-an external field. It is possible to compute the average value and the correlation functions of the acceleration of a particle in a state quite straightforwardly.
No, that isn't correct: The operator O{x(t)]= d^2 x(t)/dt^2 can be defined and its average value, in any state can be calculated. Its (time ordered) correlation functions,, likewise-just as is the case for the position operator, velocity operator, energy operator (Hamiltonian) and so on. From these correlation functions one can, then, reconstruct the probability density of the acceleration.
10th Oct, 2015
André Michaud
Service de Recherche Pédagogique (SRP Inc)
Acceleration implies localization and progressive motion of the electron, which is something that QM cannot represent, because with QM, a particle is considered localized only when the wave function collapses, which corresponds to the electron not moving.
Other than that, if we envision the electron as remaining localized when moving, then acceleration by definition involves progressive acquisition of energy. So when a photon instantaneously (presumably) transmits all or part of its energy to such an electron which would cause it to jump to an orbital further away from the nucleus, the acquisition doesn't seem to be progressive.
If such a localized electron in motion is seen as having inertia in relation to its known mass, it would be interesting indeed to determine whether or not the notion of "acceleration" applies, and if it does, how?
I'd be interested in knowing if this has been studied in the past and where such analysis could be found.
Very good question Vishnu.
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