why doesn't the electron fall into the nucleus!?

malawi_glenn

He didn't explain this in QM-terms, since the properties are found by solving the schrödinger equation - not by applying the HUP in this way. HUP is just a statistical statement of observables.

Yes, but one can not say that when the electron is closer to the nucleus, it has more KE, etc, since such statements of the electron is meaningless in QM.

No Yukawa did not use the uncertainty principle, he did advanced quantum field theoretical calculations. Which I actually went through this weekend...

malawi_glenn

i) you should not in one sentence disprove QM and in another one praise feynman and yukawa

ii) The atoms has NOT definite size, its "size" is a statistical statement. Like the root mean radius square and mean radius etc, only "mean" no "definite".

can you stop with this circus? It is clear to me that you have never studied QM from a textbook used in college...

granpa

why doesnt the earth fall into the sun?

malawi_glenn

not a perfect analogy, since a radial accelerating (non quantum) CHARGE will emit radiation and hence loose energy and decrease its radial distance.

Dadface

Take it back to basics and look at what an electron actually is.The electron has a rest mass and can display a relativistic mass increase.This fact alone appeals to intuition and leads us to imagine the electron as being a particle.The particle model may be over simplistic but it still has a tendency to persist in the mind even,I suspect, occasionally in the minds of some of the most able practitioners of QM.The particle model has its successes but also has its limitations as evidenced by the discussion here.
Let's stick with the particle model for a moment and pick up on granpas "non perfect" but neverthless relevant analogy....."why doesn't the earth fall into the sun?"and let us now apply this to the electron and ask again "why does the electron not fall into the nucleus" Let the nucleus and the electron be at a position of momentary rest and about to approach under the influence of the Coulomb force.Using just the particle model we might predict that the electron and nucleus eventually collide and make actual contact.Good, but this is not what we observe the reason being that the particle model breaks down and we have to resort to the more powerful wave model and QM.QM,QED and the like may not appeal to intuition but nevertheless they work.Whether or not there will come a greater reconciliation between particle and wave remains to be seen.

alxm

I don't have a problem with saying that. The kinetic-energy operator then, operating on the electronic wave function, increases as [tex]r \rightarrow 0[/tex]. If it didn't, the wavefunction would diverge, since the potential diverges there.

Now, unlike a classical particle, knowing the kinetic energy at any point in space requires knowing its kinetic energy at every point in space. And it the electron doesn't have a definite position and so on and so forth.

But as long as you recognize that you're not dealing with a classical particles and so on, I don't see a problem. I doubt most chemical physicists would take issue with a statement like "electrons move faster near the nucleus", although they'd no doubt prefer the more relativistically-correct "have higher momentum" to "move faster".

Halcyon-on

The interpretation given by Bohr is that the electron must follow orbit with an integer number of periods, that is only periodic orbits are allowed.

Count Iblis

No, according to Bohr Sommerfeld theory (a.k.a. "Old Quantum Theory"), the integral of P dQ integrated over a periodic orbit where P is the conjugate mometum to Q is a multiple fo Planc's constant. So, if you take Q to be the angle then the conjugate momentum is the angular momentum. Then, since for a circular orbit, the angular mometum is conserved we have:

L* 2pi = n h -------->

L = n h/(2pi) = n hbar.

f you then consider a classical orbit and the you only allow angular momenta that satisfy the above quantization rule, you find the equations for the Bohr orbits.

Since this is already too complicated to explain in the dumbed down high school physics classes, what they do is they use de-Broglie matter wave hypothesis (which came after Bohr Sommerfeld theory) and then they derive the result obtained by Bohr (who frst simply posulated that L is quantized and later with Sommerfeld came up with Old Quantum Theory).

But then it is incorrect to say that this is the derivation pesented by Bohr. So, I guess that Warren Siegel was too mild in this criticism of introductory physics textbooks, as these textbooks apperently don't even get the history correct.

Halcyon-on

Good to know! I have many other item to add to the Siegler´ s list!

Concerning the atomic orbits, the Bohr Sommerfeld condition can be formulated in energy-time rather that in momentum-space, in fact the waves are classic and on-shell. The intagral along the orbits of duration t is simplified being the energy constant. The resultin condition is

E t = n h

in this way you avoid the assumption of circular orbits. Morover from de Broglie E = h v (v=1/T is the frequence and T the period of the n-th orbital) you get
v t = n -> t = n T
and finally you see that the duration of the orbits is such that it contains a integer number of orbits. So the fundamental idea came from de Broglie, but there is an additional periodicity condition.

Here n is the atomic number. The quantization of the angular momenta is a consequence of the periodicity coming from the spherical symmetry of the problem (theta = theta + 2 pi ) whereas the spin can be interpreted as antiperiodicity of the electron wave. In this semi-classical way many other non-relativisitc quantum problems can be solved. (examples http://people.ccmr.cornell.edu/~much...feld/notes.pdf )

alxm

Well, semiclassical models have their uses, but they fail in general pretty miserably at describing atoms and molecules, with the sole exception of the Bohr model, really.

Perhaps you'd be interested in reading about some recent toyings with a semiclassical colinear helium model. They 'cheat' in a few ways (as does the Bohr model), but it's surprisingly good given the model.

But in general, semiclassical attempts at atoms/molecules are a dead end. E.g. the Thomas-Fermi model cannot form stable molecules. I doubt any semiclassical theory can, given the importance of exchange energy in chemical bonding.

feynmann

No one is saying in one sentence disprove QM and in another one praise feynman and yukawa. What was disproved is "Copenhagen Interpretation", not Quantum mechanics.
The probability of wavefunction is "Copenhagen Interpretation", Not "Quantum Mechanics" itself. There is No probability of wavefunction in Bohm's version of Quantum Mechanics

It's clear your knowledge of quantum mechanics is full of nonsense, since you don't even know the difference between quantum mechanics and "Copenhagen Interpretation", what a "Science Advisor". Would you stop calling yourself "Science Advisor"? I certainly don't need your "advice".

alxm

Wrong. [tex]|\psi(\mathbf{x},t)|^2[/tex] is a particle's spatial probability density in quantum mechanics. Regardless of the interpretation.

Maybe you should actually study the basis of the Bohm interpretation of which you speak before making such claims, in particular since I already explained this once.

The Copenhagen interpretation amounts to the claim, that that probability is truly random, i.e. indeterministic, rather than a result of incomplete knowledge of a deterministic system. i.e. hidden variables - such as the Bohm interpretation.

If you have some issue with how you can describe a deterministic system can be described in a probabilistic/statistical way, then your misunderstanding is with statistical mechanics, not QM.

ajw1

But when using the probability wave as answer for the question of the TS it seems to me that one needs the Copenhagen interpretation of this wave, being that the particle realy is 'spreadout' in it's wave (in superposition).

When one images the electron being like a fly circling around in a room one can calculate a probability wave for the fly being somewhere, but there is a great chance he finaly will be caught by the sticky strip in the middle.

Modman

This is similar to the question to the question: "Why doesn't the Earth fall into the Sun?". In both, the answer is that the revolving object has enough inertia to prevent it.

Also, there is a confusion over quantum physics. While we hold Heisenberg's uncertainty principle to be true, this does not mean we do not know what they do in there. Think of the uncertainty principle as a veil over a fitting room: we know what goes on inside the fitting room, but we cannot see it without violating a law (physics or US) .

ytuab

Quantum physics replaced Bohr-Sommerfeld theory in 1920's.
Since then many phsicists such as Pauli, Heisenberg, Dirac... have given up explaining the
motion of an electron concretely.

because by equating the angular momentum of the spinning sphere of the electron to 1/2
h-bar, the sphere speed leads to about one hundred times the speed of light.

The orbital angular momentum of the electron in the ground state of the hydrogen atom is zero, so the Coulomb potential is infinitely negative when the electron is close to the nucleus.

thoughtgaze

I don't know why people keep using this reasoning. Clearly the earth/sun analogy does not work at this level ELSE IT WOULD DEFINITELY FALL INTO THE NUCLEUS!!!!

malawi_glenn

I perfectly know the difference, it is custom to drop to the "copenhagen interpretation", since that is the standard in physics today. As we had in another thread "only amateur worries about different interpretations". So QM and Copenhagen interpretation of QM are interchangeable to many (almost all) physicists.

So let us go back to the atom again, it has no definite size, this is an experimental fact as well. If you claim that the atom has a definite size, you should have it backed up with articles. Claim was "hydrogen atoms has definite size. It's size is about the Bohr's radius", now prove it. Also you used the word "superposition" for continuous variable, position, I don't believe that makes sense in Real Analysis...

So let us go back to Yukawa again. You said that Yukawa used the heisenberg uncertainty relation to show that the strong force is mediated by pions. That is an insult to Yukawa, we actually went through Yukawa's theory in my quantum field class recently, and there is no Heisenberg principle used what so ever, just pure and nice Quantum Field Theory. Many popular science book uses Heisenberg to explain alot, even yukawa's theory, so one will, as you just proved, get the impression that it is used. But now you encountered an Science Advisor, who knows the things we are discussion in detail, since he has worked with these things, not just read them on wikipedia.

One also uses the Heisenberg principle in discussion about Feynman diagrams and virtual particles, but these "explanations" are never used in REAL textbooks. In REAL textbooks, one presents the REAL arguments. The reason for why Heisenberg principle is so applicable to explanations of quantum phenomenon is that is really easy to do so, it is really "the ultimate probabilistic" entity. It is almost like the good ol "God of the gasps", whenever one couldn't find an explanation due to lack of knowledge, one "blaimed" God. Today, people who does not know quantum mechanics uses Heisenberg Uncertainty principle for their explanations...