# Electron in a potential well

1. Jun 19, 2009

### eoghan

Hi! Let's suppose an electron in a mono-dimensional potential well. According to Heisenberg uncertainty principle, if L is the length of the well, then I have a momentum greater than $$\frac{h}{L}$$, which means that the electron has a velocity (and so a kinetic energy) greater than $$\frac{h}{L*m_e}$$. If I "press" the well, L becomes smaller and smaller, so the kinetic energy of the electron becomes greater and greater; according to the conservation of energy, the electron must take this energy somewhere: where does the electron take the energy needed to increase its kinetic energy?

2. Jun 19, 2009

### Bob_for_short

You "press" so you yourself provide the energy. If you do it sufficiently slowly, the ratio energy/frequency remains constant (an adiabatic invariant).

Bob_for_short.

3. Jun 19, 2009

### eoghan

But the energy used to press the wall is used to press the wall... I mean, the energy is used to make the atoms of the wall nearer, increasing their potential energy. So the energy I use to press the wall it's transformed in potential electrostatic energy and doesn't affect the electron

4. Jun 19, 2009

### Bob_for_short

No, if the walls are neutral, then there is no interaction potential between them. They serve just to reflect the electron so they are under pressure of the electron wave.

5. Jun 20, 2009

### eoghan

Sorry.. I don't uderstand... what do you mean by "to be under pressure of electron wave"?

6. Jun 20, 2009

### Bob_for_short

For simplicity imagine a classical particle reflecting from the left and right walls. It makes pressure on walls and likewise.

7. Jun 21, 2009

### eoghan

Ah, ok... do you mean something like a radiation pressure?

8. Jun 21, 2009

### Bob_for_short

Yes, the radiation pressure in a limited system (with reflecting walls) is of the same nature.

9. Jun 21, 2009

### feynmann

That's the so-called Zero-point energy. You can get it for "free". see this page: http://www.scientificamerican.com/article.cfm?id=follow-up-what-is-the-zer [Broken]

What is the 'zero-point energy' (or 'vacuum energy') in quantum physics? Is it really possible that we could harness this energy?

Last edited by a moderator: May 4, 2017
10. Jun 21, 2009

### malawi_glenn

No HUP is about the statistical outcome of measurments, not quantum equation of motion. The quantum equation of motion is governed by the Schrödinger Equation.

11. Jun 21, 2009

### malawi_glenn

The zerop point energy is per definition the lowest energy a system can have, thus we can not "use" it, e.g. we can not de-excite the hydrogen atom further down than it's ground state.

Last edited by a moderator: May 4, 2017
12. Jun 21, 2009

### eoghan

Well, but does the electron actually accelerate or doesn't?

13. Jun 21, 2009

### Bob_for_short

Electron (or any other particle) in the ground state is a standing wave of the lowest harmonic. It should exist. If there is no wave, there is no electron and there is no wave equation for it.

You can think without contradiction that the electron do not accelerate in the ground or in any excited state. It "accelerates" and radiates while transitions from one state to another.

Bob.

Last edited: Jun 21, 2009
14. Jun 21, 2009

### malawi_glenn

define acceleration in quantum mechanics...

15. Jun 21, 2009

### Naty1

According to HUP, things just don't like to be confined and become more and more agitated when attempts are made to confine them in ever smaller containers of any type.

One way to think about this: According to E = hf , energy increases as frequency does which means wavelength decreases; as a container is made smaller the wavelength of the contained particle is forcefully decreased....hence it's energy is forced to increase....it becomes more and more agitated

I'm unsure if vacuum energy is a source; I have always wondered if we really don't understand it whatsoever and the discovery of massive amounts of dark energy has just made me more suspicious....anyway, the work done to increase the pressure by making the container smaller seems more appealing....

16. Jun 21, 2009

### malawi_glenn

HUP is about the statistical outcome of measurements, not energy levels....

17. Jun 22, 2009

### Born2bwire

More importantly, it relates the statistical standard deviation in the measurements, not the magnitude of the mean of the measurements.

18. Jun 22, 2009

### malawi_glenn

That is correct

19. Jun 25, 2009

### Bob_for_short

The Casimir effect (kind of Van der Waals force) is too weak to be harnessed, in my opinion.

I would like to give my own view on the "zero-point" or "vacuum" energy. Normally they say that the vacuum field fluctuations exist in the vacuum. In my opinion it is not exact since, for example, the quantized electromagnetic field is in permanent "interaction" with electrons (or charges). So it is more naturally to consider them as "fluctuations" in a compound system charge+EMF. Such a model of charge-field coupling (an electronium) has been advanced in "Reformulation instead of Renormalizations" and in "Atom as a "dressed" nucleus" by Vladimir Kalitvianski available in arXiv. The vacuum field wave functions are similar to the ground state atomic wave functions which also describe a compound system (an atom). Each charge has its own quantum EMF oscillators just like each nucleus in atoms has its own electrons around. This physical model seems unusual first but quite natural after analysing the atom description reported in Atom as a "dressed" nucleus". These "atomic" results are correct but are still rather unknown.

Bob_for_short.