quantum mechanics

Thread Starter

magnet18

Joined Dec 22, 2010
1,223
OK, so what I'm confused about is things like tunneling.
an electron goes from one side of a barrier to the other. without actually crossing it.

so what happens? from what I can tell of the universe it that things don't simply disappear.
go from matter to energy, sure. but disappear and reappear doesn't make sense.
Do they go into a 4th dimension or something?
 

BillO

Joined Nov 24, 2008
992
OK, so what I'm confused about is things like tunneling.
an electron goes from one side of a barrier to the other. without actually crossing it.

so what happens? from what I can tell of the universe it that things don't simply disappear.
go from matter to energy, sure. but disappear and reappear doesn't make sense.
Do they go into a 4th dimension or something?
Unfortunately we don't know. QM gives us the probability it will happen, but gives us no idea how it happens.

In fact, the similarity of the QM Hamiltonian (which has basically no physical interpretation) to the CM Hamiltonian (which almost fully describes the system) has led to some interesting speculations.

So... Your guess is as valid as anyone's.
 

steveb

Joined Jul 3, 2008
2,431
OK, so what I'm confused about is things like tunneling.
an electron goes from one side of a barrier to the other. without actually crossing it.

so what happens? from what I can tell of the universe it that things don't simply disappear.
go from matter to energy, sure. but disappear and reappear doesn't make sense.
Here is a common sense explanation for something that defies common sense.

http://www.youtube.com/watch?v=6LKjJT7gh9s
 

russ_hensel

Joined Jan 11, 2009
825
Actually it does go through it. That is the wave function is non-zero inside the barrier ( expotential decay as I recall ). You need to look at the solutions to the schrodering (sp ) equation to begin to understand it.
 

amilton542

Joined Nov 13, 2010
496
OK, so what I'm confused about is things like tunneling.
an electron goes from one side of a barrier to the other. without actually crossing it.

so what happens? from what I can tell of the universe it that things don't simply disappear.
go from matter to energy, sure. but disappear and reappear doesn't make sense.
Do they go into a 4th dimension or something?
There is temptation in particle physics associated with the graviton, where dimensions above the third degree could be considered.
 
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Thread Starter

magnet18

Joined Dec 22, 2010
1,223
Actually it does go through it. That is the wave function is non-zero inside the barrier ( expotential decay as I recall ). You need to look at the solutions to the schrodering (sp ) equation to begin to understand it.
so, it goes through it measurably, but without interacting with it in anyway?
 

russ_hensel

Joined Jan 11, 2009
825
so, it goes through it measurably, but without interacting with it in anyway?
What do you mean by interact? What is your picture of a potential barrier? We usually compute the function of the particle, not the structure of the barrier.
 

Thread Starter

magnet18

Joined Dec 22, 2010
1,223
What do you mean by interact? What is your picture of a potential barrier? We usually compute the function of the particle, not the structure of the barrier.
By barrier I mean the insulating metal oxide in a MOSFET
Like, it goes through the barrier and has a waveform and stuff, but dosen't actually leave any kind of mark or scratch on the barrier (obviously not literally, but not metaphorically either)

New related questions
does it take time for the electron to cross the barrier?
Does the electron exist in the barrier at all at any point in time?
 

BillO

Joined Nov 24, 2008
992
Be careful about assigning any physical meaning to the wave function. The interpretation of it's square is that it gives the probability of a particular event happening. The event could be finding an electron in the barrier. If the wave function falls off sharply in the barrier, then it's square will be very small. The common interpretation of this would be that it is unlikely to find it there.
 

thatoneguy

Joined Feb 19, 2009
6,349
Remember, most of an atom is nothing. The electron cloud is just that, a cloud of probability of where the electron may be.

How could a cloud get scratched?
 

Thread Starter

magnet18

Joined Dec 22, 2010
1,223
I know that a cloud can't be scratched :p
atomic structure is one of my favorite subjects, but I was just meaning it has no interaction with any of the atoms nor their electrons inside the barrier, yet passes through it...
 

thatoneguy

Joined Feb 19, 2009
6,349
An electron is very tiny and can fit in the "cloud" of electrons forming the lattice of the metal they pass through. It would be something like fitting mercury in between Venus and the Earth without hitting anything, in a very vague approximation, the nucleus would be about Earth's orbit, so Mercury going between say Venus and Earth's Orbit without coming close enough to another electron to be repelled. Chances are low, but it is possible.
 

Thread Starter

magnet18

Joined Dec 22, 2010
1,223
OK, so that makes sense, but if it slides through without touching anything, why does it's energy decrease?
 

Wendy

Joined Mar 24, 2008
21,840
I may be misreading your post, but the further out the electron is, the more energy it has. Think about lasers, when an electron falls to a lower level it gives off a photon, when it absorbs a photon it jumps up a level.
 

russ_hensel

Joined Jan 11, 2009
825
The oxide is not really well modeled as a simple step barrier, to calculate the movement of the atoms ( and electrons.... ) in it you would need much more detail. I expect there is a non 0 probability of displacing these atoms and scratching the oxide.

Time to cross the barrier: I can think of 2 approaches. The usual model is a plane wave ( not normalized to 1 ) which gives a time independent solution. But you can compute the probability flux inside the barrier. This is more computation than I am up for right now -- my intution does not give me a good hint as to the result. The other way is to make up a wave packet which unlike the first approach is well localized in space. Computations are now probably harder.

The simple question is does the electron exist inside the barrier. Yes the probability of finding it at any point is just the square of the absolute value of the wave function.
 
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