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btw im guessing since the alpha particle is so heavy it wont be affected much by an electron moving at a moderate speed.

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- #1

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btw im guessing since the alpha particle is so heavy it wont be affected much by an electron moving at a moderate speed.

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Supose you have an atom trapped by an harmonic potential. Then you send light on this atom. Light is an electromagnetic wave. The quantum spatially extended atom will experience the light's electromagnetic forces in a extended way as well. In other words: the atom will not in general experience the electromagnetic field in just one point of space at a given instant. The ratio between the wave vector k and the width of the fundamental state of the atom inside this hamonic potential [itex], \Delta x [\itex], will give us a notion of how point-like is the interaction between the atom and the light. This parameter is the so called Lamb-Dicke parameter.

This question is somewhat related to the dipole approximation, but I believe strongly it is not the same notion.

Although the systems are not the same, I hope this serves as a begining.

Note: As long as you can treat the alpha particle as the source of a potential, it seems that you can profit from Schroedinger's equation for the electron in order to obtain the time evolution of its wave function.

Best Regards,

DaTario

This question is somewhat related to the dipole approximation, but I believe strongly it is not the same notion.

Although the systems are not the same, I hope this serves as a begining.

Note: As long as you can treat the alpha particle as the source of a potential, it seems that you can profit from Schroedinger's equation for the electron in order to obtain the time evolution of its wave function.

Best Regards,

DaTario

Last edited:

- #3

reilly

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Localized or spread out, all can be handled. This is done in any text on basic scattering theory, classical or quantum.

regards,

Reilly Atkinson

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box said:

btw im guessing since the alpha particle is so heavy it wont be affected much by an electron moving at a moderate speed.

The wavefunction is a function of the coordinates of both particles

and must be interpreted as in the following language: the amplitude

squared of the wave function is the probability that particle A is at x1

AND particle B is at x2. It is a joint probabliity distribution.

Of course this language is overly simplistic. One particle could be in a state

of definite momentum with equal amplitude everywhere in space. This is

why the Psi function is considered to have only a probabilistic interpretation

and not a directly physical one.

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