# Wave function of particles approching 0 K

1. May 23, 2014

### nehorlavazapal

Am I right to think that particles cooled asymptotically to 0 K would have wave functions the size of galaxies or even larger (provided they would stay cooled long enough for that light cone---).

2. May 23, 2014

### Staff: Mentor

0 K is the ground state assuming it is not degenerated. This can still have a finite energy if the material is trapped somewhere. It does not need to spread out so large.

3. May 24, 2014

### nehorlavazapal

Yes, of course. I was only asking if it is possible in theory..at let's say 10^-20 K. For example if vacuum fluctuations would collapse the wave function into a smaller volume.

4. May 24, 2014

Staff Emeritus
Please reread mfb's answer. 0K does not mean zero energy, it means minimum energy.

5. May 24, 2014

### nehorlavazapal

Yes, please forgive me if I am missing sometihing: I would rather reformulate my question: are there any fundamental bariers that would prevent a small macroscopic agregate (like 10^6 atoms) from having a 95 % probability of being inside a galaxy via extremely low associated energy? For exampe is there any fundamental real limit on the "bond energy" inside that atomic cluster?

6. May 24, 2014

### Staff: Mentor

All our atoms are within our galaxy with (practical) certainty.
To get the wavefunction of a particle (or even a set of particles) spread out over the scale of a galaxy, you would have to switch off all interactions with other particles. There is no known way to do that.

7. May 24, 2014

### QuasiParticle

The answer by mfb is very good.

The thermal de Broglie wavelength of non-interacting particles becomes infinite as temperature approaches zero.

8. May 25, 2014

### nehorlavazapal

Yes, that's what I have meant. Are there any particles that would come close.. like a few kilometers, i.e. very cold neutrinos or WIMPs?

9. May 26, 2014

### Staff: Mentor

Photons can easily do that. Use a flashlight and point it towards the sky. That's not in thermal equilibrium then, of course.
I guess neutrinos can work as well.

10. May 26, 2014

### ChrisVer

Well the ground state of the harmonic oscillators for example, doesn't have 0 energy, and so it won't have 0 temperature...
$[E]=[k_{B}][T]$
So how can we say it can reach for example T=0 at GS?

11. May 26, 2014

### Staff: Mentor

Zero energy has nothing to do with zero temperature.
Actually, "zero energy" is an arbitrary definition. Zero temperature is not, it is defined via entropy.
Your equation just matches with units, but not with the physics.

12. May 26, 2014

### QuasiParticle

I'm not quite sure what you are after. Cooling and thermalizing neutrinos is not possible. What first comes to my mind as an example of macroscopic quantum behavior is liquid He-4 at low temperatures. In a many-body system of identical bosons, the system condenses to its lowest energy state at some low temperature and the particles lose their identity (Bose-Einstein condensation for non-interacting particles). The onset of this transition usually occurs when "the wave functions of the atoms begin to overlap", i.e. when the thermal de Broglie wavelength is of the order of the interatomic separation. Superfluid He-4 can be described by a macroscopic wave function. And actually the dimensions of the container begin to limit the properties of the system.