# Will a single electron in vacuum vibrate?

1. Jan 24, 2007

### K.J.Healey

If so why? What is the spring force that keeps the vibration mode going. I know quantum mechanics, but I don't know if i've ever thought about this specific instance. A single electron, can it have vibrational energy (T & U) and what is its method of vibration.

Thanks for clarifying this.

2. Jan 26, 2007

### Werg22

The particle-wave nature of all matter tells us that everything vibrates. Even you.

3. Jan 26, 2007

### vanesch

Staff Emeritus
It depends what you mean by "vibrating". If we assume a free, flat space, with a single electron in it, in a certain energy-momentum state, well, that will remain so, then (in free field theory). It is not really "vibrating", it will have the energy and momentum specified by the initial state. From the moment that we are going to "measure" something, the universe will have to contain more than one single electron ; it will need something which will act as "measurement apparatus".

4. Jan 26, 2007

### arunma

It's also important to note that the exact position of an electron is somewhat delocalized. In that sense, all small particles "vibrate." I think this may be what Werg alluded to by his reference to the wave-particle duality.

5. Jan 26, 2007

### ZapperZ

Staff Emeritus
But it is misleading to equate delocalization with "vibration". Delocalization simply indicates that one cannot make a good prediction of the exact position of the electron. Vibration, on the other hand, requires the emission of EM radiation, which we do not observe for an "electron in vacuum".

Note that when one solves for the plane-wave state of a free electron, one do not interpret the wavefunction as a "vibration" of that electron. This is entirely different than what one would get when solving for a quantum harmonic oscillator, for example.

Zz.

6. Jan 27, 2007

### K.J.Healey

Thanks ZapperZ thats what I was thinking. I know about the quantum "vibration" but thats not vibration, rather probability of measurement as I see it.
So therefor would it be true to say than an electron CANNOT vibrate as a free particle sans outside forces, or for that matter any free particle. (I chose electron due to its lepton simplicity)
That makes sense then, as I see no reason why it would be able to. I just wasn't 100% positive.
Do complete atoms have vibration in the mechanical/EM definition considering they have an electron contained in a quantum well? I'd assume so and thus also assume that an individual H atom can have multiple "temperatures"? Give it enough energy and the electron jumps energy states. But is it simply continuous or is it quantified?
What about Baryons then? Do we know enough about the forces that bind quarks together to know whether or not they can produce intra-system vibrations similar to my assumed electron-proton pair vibration?

I'm sorry if i seem to not know about some basic particle properties. I've never taken a particle/nuclear physics class(though I try to read as much as possible online), and undergraduate quantum only concerns itself with basic hydrogen style systems.

7. Jan 27, 2007

### Gib Z

Actually, its not just about our measurements. Heisenberg's Uncertainty principle applies intrinsically, measured by a conscious observer or not. Thats how nuclear fusion in our sun works.

8. Jan 27, 2007

### ZapperZ

Staff Emeritus
For a vibration such as a harmonic oscillator, one needs a potential or a force. This is rather obvious because that is what the "potential" term is in the Hamiltonian, be it a classical Hamiltonian/Lagrangian, or the quantum Hamiltonian. If this term is zero, you have a free particle!

Atoms and molecules have some "resonances". In molecules, the intra-molecular bonding can have a vibrational spectrum. However, for individual atoms, I would hesitate to equate these are "vibration". One do not solve a "vibrational" equation when solving for the energy level of an atom, because the central potential does not look like something one equate with a simple harmonic oscillator.

The bound state of quarks are way different than electromagnetic interactions. They are governed by QCD, a completely different set of rules than QED.

Zz.

9. Jan 27, 2007

### Staff: Mentor

In an atom (such as hydrogen) that is in a state of definite energy (such as the ground state), the electron has a probability distribution function that does not vary with time. We call these stationary states.

In an atom that is in a superposition of two (or more) definite-energy states (such as an atom undergoing a transition between two energy states), the electron has a p.d.f. that does vary with time. It sloshes or pulsates with a frequency that corresponds to the energy difference: $f = \Delta E / h$, which is the frequency of the light that is emitted or absorbed in the transition.

10. Jan 27, 2007

### arunma

Yes, you are correct. I hope I haven't made anyone think that the quantum uncertainty in an electron's position contributes to its kinetic energy.

11. Jan 27, 2007

### cesiumfrog

...If hydrogen falls into a star, and nobody is there to see the colour of the light, will nuclei still tunnel together and produce helium?

12. Jan 27, 2007

### Gib Z

yes?... :\ I would think so...theres alot of other stars in the universe that we don't see, and I would think that they also produce helium..