A Collapse of the electron wave function due to inelastic interactions

[Philip Koeck]

I'm wondering about phase contrast imaging with a transmission electron microscope (TEM).
It's generally accepted that phase contrast arises because scattered waves interfere with the unscattered wave when they meet again in the image plane.
It's also well established, I believe, that each electron only interferes with itself, since it's possible to decrease the beam current so much that the electrons are several mm apart on average.

If I now place a device in the back focal plane (where the diffraction pattern is located) that enhances phase contrast (a phase plate) this device could also change the energy of the TEM-electron.
For example the unscattered component of the wave could loose a small amount of energy whereas the scattered components don't, whatever that means since we're talking about a single electron here.
Would such an energy loss immediately make the wave function collapse and destroy phase contrast?

In particular the phase plate I'm thinking of consists of a dilute cloud of electrons located in the back focal plane on the optical axis of the TEM. The energy change of the unscattered electrons (with 200 keV kinetic energy, for example) is in the order of 1 meV.

 

[gentzen]

Would such an energy loss immediately make the wave function collapse and destroy phase contrast?

... The energy change of the unscattered electrons (with 200 keV kinetic energy, for example) is in the order of 1 meV.

No, it won't have a dramatic effect, and will certainly be nowwhere near to what phenomenologically could appear like a wave function collapse.

Why do I believe this? Because the energy spread of your electron source will already be significantly bigger than 1 meV. And this has basically no impact on the imaging either. Of course, one could also try to compute which impact it could have, but if the result of the computation would contradict what is already known from experience, believe me, the mistake will be in the computation, not in the experience.

 

[bob012345]

Is the wave function a physical object? If not, what is collapsing?

 

[Nugatory]

Is the wave function a physical object? If not, what is collapsing?

That depends on the interpretation we've chosen. Any further discussion of that question belongs in the Interpretations subforum - discussion here will only hijack the thread.

 

[Demystifier]

The Schrodinger equation is linear. Linearity is incompatible with collapse at a purely mathematical level, independently on interpretation.

 

[Philip Koeck]

No, it won't have a dramatic effect, and will certainly be nowwhere near to what phenomenologically could appear like a wave function collapse.

Why do I believe this? Because the energy spread of your electron source will already be significantly bigger than 1 meV. And this has basically no impact on the imaging either. Of course, one could also try to compute which impact it could have, but if the result of the computation would contradict what is already known from experience, believe me, the mistake will be in the computation, not in the experience.

Maybe I'm overthinking this, but isn't there a fundamental difference here.

The energy variation from the source or even due to the specimen doesn't allow me to locate the path of the electron in most cases.
However if I have a phase plate that can change the energy of an unscattered electron, but doesn't change the energy of scattered electrons so much, I can, in principle, know where the electron went if it lost or gained enough energy.
So, if I wanted to and had the necessary technology (spectrometer with meV resolution), I could know whether the electron was scattered or not.
Would that kill phase contrast?

 

[gentzen]

Maybe I'm overthinking this, but isn't there a fundamental difference here.

The energy variation from the source or even due to the specimen doesn't allow me to locate the path of the electron in most cases.

Of course there is a difference, but the fact that the energy spread of the electron source is significantly bigger than 1 meV nevertheless allows you to conclude that the electron optics for the detector won't be affected much. What the energy variation could do is to impact the actual phase shift, but you can include this effect in the design of the phase plate optics.

However if I have a phase plate that can change the energy of an unscattered electron, but doesn't change the energy of scattered electrons so much, I can, in principle, know where the electron went if it lost or gained enough energy.
So, if I wanted to and had the necessary technology (spectrometer with meV resolution), I could know whether the electron was scattered or not.
Would that kill phase contrast?

Careful, you are working with phase contrast here! This means that the actually used detection optics will be such that the detected single electron was both scatter and not scattered at the same time, phenomenologically. If you use a a different detection setup, which can distinguish those energy differences, then this is no longer the case. The detected electron will then either be scatter or not, phenomenologically.

But this change was cause by your detection setup, not by the phase plate slightly changing the energy of unscattered electrons.

 

[Philip Koeck]

Phase contrast in TEM relies on interference between scattered and unscattered waves. A phase plate in the back focal plane shifts the phase of unscattered electrons, enhancing contrast. If your phase plate causes a small energy loss (~1 meV), it’s unlikely to destroy phase contrast, as 1 meV is negligible compared to 200 keV. However, if it induces inelastic scattering or random energy shifts, it could degrade coherence. The impact depends on whether the energy loss is consistent or stochastic. Are you considering this for an experiment or as a theoretical idea?

It's for an actual phase plate I'm working on.

 

[Philip Koeck]

Phase contrast in TEM relies on interference between scattered and unscattered waves. A phase plate in the back focal plane shifts the phase of unscattered electrons, enhancing contrast. If your phase plate causes a small energy loss (~1 meV), it’s unlikely to destroy phase contrast, as 1 meV is negligible compared to 200 keV. However, if it induces inelastic scattering or random energy shifts, it could degrade coherence. The impact depends on whether the energy loss is consistent or stochastic. Are you considering this for an experiment or as a theoretical idea?

The energy variation is definitely stochastic.