There are many physical problems in which the acceleration causes phenomena of interest. For example, the radiation of accelerated charge. This phenomena must be, obviously. of quantum nature, but, the available descriptions start from classic principles. On the other hand, both in Relativity as in quantum physics, the accelerated systems are strongly "hard of to study". The question goes to inquiry about the state of our mathematical tools for the description of accelerated systems in quantum mechanics.
Yes off course. But, in this case, the electron is confined in a central potential and the wave functions are stationary. Thus, the system is conservative and not emits or absorbs radiation, a minus that, the stationary system is perturbed and fall at other level.
The problem is when the system is not stationary, and the eigenvalues of energy and momentum changes continually.
Is this case in that the particles are not confined, but are interacting with an accelerator potential.
In the case of an electron accelerated for an electric field. The description of the system must be included the interchange of virtual photons with the field. These virtual photons carries energy and momentum and accelerates the electron. And, for the effect of the acceleration, the electron emits detectable photons of electromagnetic radiation, losing this way a certain quantity of energy and momentum. This phenomena, can be described by means of dynamics equations and wavefunctions?
do you can tell me where?. Do you can me suggest a book or paper where this problem is well described?.
Following is a link to an article which deals with acceleration on quantum scale. It contains a new wave equation which is developed by merging Newton's inverse square law with Schrodinger wave equation. Here the particles are not in bound state / stationary state. Specific case of electron positron creation is shown in the table.
Article Periodic quantum gravity and cosmology
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