Trying to understand the interference limits of matter-wave

[tiagovtristao]

Given the de Broile wave matter equation, wavelength = plank's constant / momentum,...

1) what's the maximum distance from the electron until its wave like behaviour stops interfering with its surroundings?

2) why the bigger the wavelength, the more the electron is to interact with its surroundings?

3) why is the picture of the wave like behaviour always drawn as a wave (of probability) of only 1 cycle (its wavelength)?

4) why does it work to explain quantised levels in an atom? I know it's due to constructive interference, where the orbit circumference is equal to N*wavelength. But what does this imply? The wave like behavior/probability travels through space?

 

[DrClaude]

The de Broglie wavelength was important for the historical development of quantum mechanics, and it is still an interesting heuristic for estimating the size of quantum effects, but it is not part of modern quantum mechanics. So there is no satisfying answers to your questions.

In particular, point 3 has no physical explanation: it is "artistic liberty." In point 4, you seem to be thinking with Bohr's model, which is also obsolete.

I suggest you start learning modern quantum mechanics.

 

[tiagovtristao]

The de Broglie wavelength was important for the historical development of quantum mechanics, and it is still an interesting heuristic for estimating the size of quantum effects, but it is not part of modern quantum mechanics. So there is no satisfying answers to your questions.

In particular, point 3 has no physical explanation: it is "artistic liberty." In point 4, you seem to be thinking with Bohr's model, which is also obsolete.

I suggest you start learning modern quantum mechanics.

What do you mean by modern quantum mechanics? I thought that's when Bohr's view of the atom was replaced from the moment when matter wave was discovered, which led to numerous discoveries in the following decades. However, I'm not familiar with quantum electrodynamics, if that's what you meant. But I'd be thankful if you could point me more precisely to what I should dig into to be able to find the answers to the questions of my first post.

Thanks for your time :)

 

[DrClaude]

What do you mean by modern quantum mechanics?

I'm talking from the Schrödinger equation and beyond.

But I'd be thankful if you could point me more precisely to what I should dig into to be able to find the answers to the questions of my first post.

The point is that the there are no answers to your questions, because the questions don't make sense in the context of our current understanding. For instance,

1) what's the maximum distance from the electron until its wave like behaviour stops interfering with its surroundings?

There is no such thing as "wave-like behavior," so there is no maximum distance associate with it. And what does "interfering with its surroundings" mean? A particle doesn't interfere with its surroundings.

What is your level in math? Do you know linear algebra and calculus?

 

[m k]

The wave like behavior/probability travels through space?

Is probability physically real.

I think decay is one limit.

 

[woody stanford]

What do you mean by modern quantum mechanics? I thought that's when Bohr's view of the atom was replaced from the moment when matter wave was discovered, which led to numerous discoveries in the following decades. However, I'm not familiar with quantum electrodynamics, if that's what you meant. But I'd be thankful if you could point me more precisely to what I should dig into to be able to find the answers to the questions of my first post.

Thanks for your time :)

I have to agree with Dr. Claude here Tiago. Bohr and De Broglie were available in QM 98 Service Pack 3 but are no longer supported. I would suggest activating your compatibility mode in QFT 2010 and downgrade your screen resolution down to 640x480 and then you might get some play on these "old-school" ideas of yours.

Just saying.

 

[tiagovtristao]

There is no such thing as "wave-like behavior," so there is no maximum distance associate with it. And what does "interfering with its surroundings" mean? A particle doesn't interfere with its surroundings.

I might be using the wrong wording here. By "wave-like behaviour", I meant probability, and the same applies to "interfering". So, I'll try to rephrase my core questions...

If you have an electron close to a "thin" potential barrier, there's a small probability that it might appear (tunnel) on the other side. So, how far would the electron have to be from the barrier for this probability to be zero?

Another question... Considering the the double slit experiment where ideally one single electron is shot at a time. How wide would the slits have to be, or how far apart, for the interference fringe not to occur?

What is your level in math? Do you know linear algebra and calculus?

I do, although I might be a bit rusty. I studied Electronic Engineering where my interest in quantum mechanics sparked.

 

[bhobba]

What do you mean by modern quantum mechanics?

Ok here is the outline of the history.

In 1924 De-Broglie had the idea if waves can sometimes act like particles as in light then maybe the converse can happen - particles like electrons can sometimes act like waves. He wrote it up as his PhD thesis but the examiners didn't know what to make of it. Well a copy made its way to Einstein - this book gives the full details:
https://www.amazon.com/dp/1491531045/?tag=pfamazon01-20

He recognized immediately it was an important step in solving the quantum puzzle, but knew it was not the answer - basically it was wrong - but his intuition, correctly, told him it was a step in the right direction. He gave it his enthusiastic support. The examiners were still not convinced despite Einsteins approval, but did like the math, so he got his PhD.

Then things moved quickly. Schrodinger in giving a lecture on it was challenged - if matter was waves then it should obey a wave equation. He found one - but while he got the correct answer he made an error in doing it:
https://arxiv.org/abs/1204.0653

These days we can easily derive the so called Klein-Gordon equation from very simple considerations and the Schrodinger equation as the relativistic limit - but that is another story requiring another thread. Start one if you like.

At about the same time Heisenberg came up with his matrix mechanics. They looked entirely different. Then an upstart called Dirac came up with a still different approach called q numbers that Heisenberg recognized as better than what he did. Now things were in a really bad way. But very quickly and to everyone's surprise, even Einsteins, everything fell into place:
http://www.lajpe.org/may08/09_Carlos_Madrid.pdf

Dirac's 1926 transformation theory paper is basically QM as we know it today. But mathematically it used things that were 'dubious'. It was elegant beyond belief but mathematicians like Von-Neumann were concerned that its mathematics was not valid. He came up with a version that was mathematically correct, but physicists spoke with their feet and chose Dirac.

Well mathematicians took this as a challenge and thanks to the efforts of three of the greatest mathematicians of the 20th century, Grothendieck, Gelfland, and Schwartz the issues were all resolved and two very useful branches of math were invented - Rigged Hilbert Spaces and Distribution theory. Distribution theory especially is so useful every applied mathematician (and that very much includes electrical engineers) should know about it. It for example makes Fourier transforms a snap, otherwise it becomes bogged down in issues of convergence. If you are into Electrical Engineering (and applied math in general) I strongly recommend the following book:
https://www.amazon.com/dp/0521558905/?tag=pfamazon01-20

Einstein was proved right - De-Broglie's idea was wrong - but an important and necessary step to the right answer.

Thanks
Bill

 

[DrClaude]

I do, although I might be a bit rusty. I studied Electronic Engineering where my interest in quantum mechanics sparked.

Then you should go ahead and learn quantum mechanics. Get yourself a textbook and start reading! I'm sure you won't regret it.

 

[PeterDonis]

how far would the electron have to be from the barrier for this probability to be zero?

Strictly speaking, infinitely far; the tunneling probability decays exponentially with the distance from the barrier, so it never becomes exactly zero at any finite distance.