Interpretations of diffusion in Quantum Mechanics.

[learn.steadfast]

Recently, I've been told I was wrong concerning the nature of stationary states and diffusion being related. Even though I pointed out to the people involved that I was merely paraphrasing Max Born, who was apparently quoting the same idea as Linus Pauling.

No one has been able to tell me, however, the difference between my interpretation and Linus Pauling's or Born's.

The third edition of Linus Pauling's book, "The nature of the chemical bond" was published in 1960. I refer to this because it's the easiest reference for me to cite and people to look up in the local library, rather than an earlier work. The people who told me I was wrong cited results from Quantum Electrodynamics, which dates around 1962-1965.

I am wanting to know if QED has proven the non-relativistic interpretation made by Born and Pauling, wrong.

For, Linus Pauling writes in chapter 2-3, "Stationary States of the Hydrogen Atom"; that "Some change [eg: from Bohr] have been made as a result of the dicovery of Quantum Mechanics. The motion of the electron in the hydrogen atom according to quantum mechanics is described by means of a wave fuction $psi$ as mentioned in chapter 1. ... The Heisenburg uncertainty principle ... shows that we cannot hope to describe the motion of the electron in the normal Hydrogen atom in terms of a definite orbit..."

In Chapter 1, Linus had said: "The most probable distance of the electron from the nucleus is thus just the Bohr radius a0; the electron is, however, not restricted to this one distance. The speed of the electron is also not constant but can be represented by a distribution function, such that the root mean square speed has just the Bohr Value v0."

Linus is speaking about the 1s orbital of Hydrogen in his diagrams. The 1s orbital has no orbital momentum, and therefore isn't a classical orbit with any definite direction around the nucleus as Bohr Imagined; However, Linus Pauling makes it very clear that the electron is in motion with an average statistical speed.

Has QED proven that the motion of the particle, which in QM statistically interpreted, does not have EM fields such that the RMS speed mentioned by Pauling does not create a statistical spectrum of probable EM noise?

I think Linus Pauling is clearly describing statistical diffusion, when he says:
"We can accordingly describe the normal hydrogen atom by saying that the electron moves in and out about the nucleus, remaining usually within a distance of about 0.5 Angstrom, with a speed that is variable but is of the order of magnitude of V0."

In solid state semiconductor physics, we talk about drift speeds and diffusion speeds in Electrical Engineering courses. Diffusion speeds are described by RMS values, drift speeds are described by DC values.

Pauling mentions Heisenburg when referring to the reason a statistical orbit is required to interpret QM. But, since there is no angular momentum in a 1S orbital, the average motion of the electron can't be either clockwise or counterclockwise around the atom. It must go in both directions with equal probability. I understand that description to be of a diffusing electron, which is similar to brownian motion.

Diffusion is characterised by the time averaged net forces acting on a particle being zero. That is to say, the average (ensemble) motion of the electron has zero drift force (DC/Direct current). But, it does have an nonzero frequency component (AC/alternating current.) Hence, there *must* be a spectrum of EM fields associated with a 1S electron's motion, even if the Heisenburg uncertainty does not allow us to measure the spectrum without destroying it.

Even if the spin of the electron is taken into account, that could at most mean that the orbital angular momentum must be equal but opposite to that of the partcles rotation about the nucleus.

Yet, QM predicts that a 1S orbital has a spin of $\hbar/2$, so that the angular momentum of the electron is distinct from the 1S orbital which has no angular momentum.
eg: The spin of the electron is not canceled by it's 1S orbit, and that is proven conclusively by the Stern Gerlach experiment.

Has QED made any of the assertions I just gave, invalid?

Or, am I justified in assuming that the electron diffuses spherically in a 1S orbital, due to background radiation, thermal agitation of molecules, and "noise" disturbances to the EM field caused by the electron, nucleus, neturons, and other particles which on average do not impart a drift motion on the electron but DO cause an RMS (AC) signal and spectrum to exist?

If I am wrong, in what way am I wrong; and how is it proven using basic QM rather than relativistic QED?

 

[PeterDonis]

Linus Pauling makes it very clear that the electron is in motion with an average statistical speed.

No, what he is making clear is that if you were to measure the electron's speed, the function he describes would give you the probability of getting the various possible results. He is not saying that if the electron's speed is not measured, it still has a definite speed whose average is given by the value he cites. (Or if he is saying that, he's wrong, since that would contradict basic QM.)

the motion of the particle, which in QM statistically interpreted

Not if "statistically interpreted" means what you are claiming it means. See above.

I think Linus Pauling is clearly describing statistical diffusion

That's because you're misinterpreting what QM says about this case. See above.

Linus is speaking about the 1s orbital of Hydrogen in his diagrams. The 1s orbital has no orbital momentum

No orbital angular momentum. More precisely, an electron in a 1S orbital has no orbital angular momentum. See below.

Even if the spin of the electron is taken into account, that could at most mean that the orbital angular momentum must be equal but opposite to that of the partcles rotation about the nucleus.

Huh? Spin is not orbital motion and does not describe "the particle's rotation about the nucleus".

QM predicts that a 1S orbital has a spin of $\hbar/2$,

No, it doesn't. It predicts that an electron in a 1S orbital has zero orbital angular momentum. The orbital itself doesn't have an angular momentum; it's not a particle. It certainly doesn't have spin.

QM also predicts that an electron in a 1S orbital, such as the electron in the ground state of the hydrogen atom, has a spin angular momentum with magnitude $\hbar / 2$. (More precisely, that if you were to measure the electron's spin, you would get either $\hbar / 2$ or $- \hbar / 2$. But if the electron is bound in a hydrogen atom, you can't measure its spin in isolation; you can only measure the spin of the atom as a whole. So there are complications here that you are not taking into account. But even without taking them into account, you are clearly confused about how orbitals work.)

the angular momentum of the electron is distinct from the 1S orbital which has no angular momentum.

The spin angular momentum of the electron is distinct from its orbital angular momentum. Yes, that's correct. It's an obvious consequence of the definitions of spin angular momentum and orbital angular momentum. So what?

The spin of the electron is not canceled by it's 1S orbit, and that is proven conclusively by the Stern Gerlach experiment.

The Stern Gerlach experiment did not measure the spin of electrons in a 1S orbital. It measured the spins of silver atoms that had one unpaired electron, so the spin of the atom as a whole was assumed to be equal to the spin of the unpaired electron. But the unpaired electron was not in the 1S orbital. (It was in an S orbital, at least in the simplest version of the experiment, but not 1S.) Also, this analysis ignores the spin of the nucleus (that's one of the complications I referred to above).

am I justified in assuming that the electron diffuses spherically in a 1S orbital, due to background radiation, thermal agitation of molecules, and "noise" disturbances to the EM field caused by the electron, nucleus, neturons, and other particles which on average do not impart a drift motion on the electron but DO cause an RMS (AC) signal and spectrum to exist?

No, you're not justified. Both standard non-relativistic QM and QED agree that the ground state of a hydrogen atom is a stationary state; that means nothing is changing. Diffusion of the kind you are talking about would be a change.

Anyway, if you were correct, hydrogen gas, for example, would emit an RMS AC signal and spectrum. But it doesn't.

 

[PeterDonis]

Since the OP is rehashing a topic which has already been closed once, this thread is closed.