De Broglie Hypothesissome questions

[Physicist]

De Broglie Hypothesis..some questions!

Hi all,

I need to understand more about De Broglie Hypothesis.

How can I imagine the wave associated with the particle? I always imagine that the particle is moving in a path having the shape of a wave... I think this is wrong but I couldn't imagine it in a different way..

Also, I want to know what is the relation between the De Broglie wavelength of atoms & the spacing between these atoms?

I read that if the atoms' De Broglie wavelength is small compared to the spacing between them then we can describe them using classical physics.. I couldn't know why?

Can anyone help?

Thanks

 

[selfAdjoint]

The wave or particle nature depends on how you observe it, or in general how it interacts. Some observations depend on the wave length, like the double slit that produces interference fringes. Others depend on the momentum, the usual example at intro level being the photoelectric effect. Quantum mechanics is all about doing experiments and seeing what happens, and what happens depends on what experiment it was.

It is a very good thing to distinguish the wave nature from the wave function. The wave nature, as I just said, is an observable property. The wave function is not observable itself, it just generates a probability to have some observable property.

 

[dextercioby]

Also, I want to know what is the relation between the De Broglie wavelength of atoms & the spacing between these atoms?

It's quite difficult to find the wavefunction (which contains wave-like elements of a particle) for an atom in interaction with other ones...

I read that if the atoms' De Broglie wavelength is small compared to the spacing between them then we can describe them using classical physics.. I couldn't know why?

Where did u read that...?Atomic/molecular world cannot under any circumstance be described by classical physics...

Daniel.

 

[Physicist]

Thanks for answering.

Where did u read that...?Atomic/molecular world cannot under any circumstance be described by classical physics...

I read that in http://cua.mit.edu/ketterle_group/Projects_2002/Pubs_02/angl02_nature_insight.pdf, you can find it in the 2nd paragraph - 1st column - 1st page.

Maybe I understood something wrong! So I will be thankful if u can explain more to me.

Regards.

 

[selfAdjoint]

Thanks for answering.



I read that in http://cua.mit.edu/ketterle_group/Projects_2002/Pubs_02/angl02_nature_insight.pdf, you can find it in the 2nd paragraph - 1st column - 1st page.

Maybe I understood something wrong! So I will be thankful if u can explain more to me.

Regards.

That paragraph says this:

The essential techniques for making quantum-degenerate
gases are cooling techniques, because at high temperatures
a dilute gas of atoms behaves classically. As long as the
atoms’ de Broglie wavelength ldB4ù/(2MkBT)1/2 is small
compared to the spacing between atoms, one can describe
their motion with classical trajectories. (ldB is the position
uncertainty associated with the thermal momentum
distribution, and increases with decreasing temperature T
and atomic mass M.) Quantum degeneracy begins when ldB
and the interatomic distance become comparable. The
atomic wave packets overlap, and the gas starts to become a
‘quantum soup’ of indistinguishable particles. If the atoms
are bosons, a condensate — a cloud of atoms all occupying
the same quantum state — appears at a precise temperature

Showing a transition from classical description to quantum degeneracy. Perhaps you just misstated the fact that the world where the Compton wavelength is not ignorable relative to the physical spacing is not a classical one. The same gas could be treated classically and quantally at two different temperatures.

 

[ZapperZ]

Thanks for answering.



I read that in http://cua.mit.edu/ketterle_group/Projects_2002/Pubs_02/angl02_nature_insight.pdf, you can find it in the 2nd paragraph - 1st column - 1st page.

Maybe I understood something wrong! So I will be thankful if u can explain more to me.

Regards.

The "overlap" they are talking about is NOT the overlap of the atom's "deBroglie wave", but rather the ATOMIC wavefunction. When you solve the Schrödinger equation for an atom, you obtain the atom's wavefunction containing the atomic orbitals. When atoms are close enough to each other, the atomic orbitals, especially the valence shell, will overlap. If there is significant overlap, they each become indistinguishable, and this is where the nature of their spin matters and quantum statistics kicks in.

Zz.

 

[marlon]

Hi all,

I need to understand more about De Broglie Hypothesis.

How can I imagine the wave associated with the particle? I always imagine that the particle is moving in a path having the shape of a wave... I think this is wrong but I couldn't imagine it in a different way..

The particle wave duality has already been explained here. I just wanted to add the notion that this duality is NOT inherent to QM. I mean, if we would live in a QM-world, this duality would not exist because we would not know the notion of particle and wave. The duality only exists because we look at QM and its results with our "classical" eyes. So the duality only exist because we think in terms of waves and particles, however you do not need this knowledge to work with QM in itself...

marlon

 

[dextercioby]

Maybe a course on Statistical Mechanics and one on Solid State Physics would help clear up a bit this quite interesting part with degenerate quantum gases and the possibility of applying Boltzmann statistics...

Daniel.