What exactly is electron tunelling?
When an electron is kept inside a closed container it is said that
there is a probablity of it tunneling through space-time and appearing
somewhere else between + infinity and - infinity.
How will it travell through space time ?

DARTH VADER wrote:
What exactly is electron tunelling?


http://www.google.com/search?q=electron+tunelling

DARTH VADER wrote:
What exactly is electron tunelling?
When an electron is kept inside a closed container it is said that
there is a probablity of it tunneling through space-time and appearing
somewhere else between + infinity and - infinity.
How will it travell through space time ?

This is true, though not only of electrons, but for any quantum
mechanical object. Even things as large as animals and planets have
some probability of tunneling, though it gets pretty practically close
to zero for anything larger than an atomic nucleus.

Quantum mechanics goes like this: Given a system in state S at time
T, what state S' can be expected at T'? In classical physics the answer
is that S implies one and only one consequence, S'. In QM, however, an
entire spectrum of possible outcomes is possible. S at T implies, at
T', {...S1,S2,S3,...}. In fact there may be an infinity of possible
outcomes.

But not all possible changes of state have equal probability. Their
respective likelyhoods may be plotted on a graph:

P
R
O
B
A
B
I S8 S9
L S7 S10
I S6 S11
T S5 S12
Y S4 S13
...S1 S2 S3 S14 S15 S16...

The probability function is the absolute square of what's called the
'wave function' for the system in question, and the wave function is a
function of the relevant physical variables which define the system.
But let's say there's an electron trapped inside a magnetic toroid. (A
kind of donut shaped magnetic bottle, like they might use to store
anti-matter on Star Trek.) For the electron there's a wave function
that defines the likelyhood of it being detected within some spatial
interval. The peak of that function lies within the trap, but the left
& right tails of the curve extend a lot farther afield, in fact right
out of the trap itself. So there's some small probability of the
electron being detected outside. If so, then it's said to 'tunnel'
through the barrier, in a fashion never expected or allowed by
classical physics.

For a single such particle you might not reasonably expect to ever
detect it outside. But let's say the probability is 1/10^20 for a time
interval of delta-T. If you stuff the containment barrier with at least
10^20 electrons, then within a period equal to delta-T, you can
reasonably expect at least one of the electrons to tunnel through. This
is actually how alpha-radioactivity is understood to work. For atoms of
very large atomic number the nucleus is a large package of protons &
neutrons. The outer nucleons act as a barrier to the inner ones. But
they have a defined likelyhood of tunneling through and escaping. It
turns out to be respectably high for systems of two protons & two
neutrons. This is the alpha particle which tunnels.

And it's not precisely that, in standard QM the particle literally
travels through walls. It's more that the particle's position isn't
well defined to begin with. It exists *everywhere* within the area
addressed by its wave function. By placing a measuring apparatus within
an electron's region of possible locations, the electron is made to
either **** or get off the pot. So it ****s, meaning that it interacts
with the system comprising the device, and a location is registered by
the device.

-Mark Martin

The tunneling distance is limited to the size
of the electron's wave. Therefore it is very short
range.

Mass doesn't leak more than a microscopic
distance. Hawking is wrong!!!

wrote:
The tunneling distance is limited to the size
of the electron's wave. Therefore it is very short
range.

Mass doesn't leak more than a microscopic
distance. Hawking is wrong!!!

You know what Nick? All he asked about was "tunneling". He didn't
ask about Hawking radiation. But you have to take every opportunity to
inject your agenda into any & all conversations. You know what Nick?
You're a selfish slob. Excuse me, I have to go take a Nick.

-Mark Martin

Yes it is selfish of me to point out that Hwaking is wrong!!!

wrote:
Yes it is selfish of me to point out that Hwaking is wrong!!!

(*chuckle*) If only you had, it might be a point in your favor. As
it is, all you even said is that tunneling has a low relative
frequency, but not zero. If you were to privide some convincing
calculations indicating that the rate of black hole emission must be
negligibly small, then you've got yourself an argument. But alas, all
you'll ever do is sputter your baseless assertions. You're a worthless
piece of Nick.

By the way, who exactly is "Hwaking"?

-Mark Martin

"DARTH VADER" wrote in
oups.com:

What exactly is electron tunelling?

In classical physics, if a particle has energy A and it needs energy B to
get past a barrier, and A is less than B, then the particle simply won't
get past the barrier. This is true even if A is "close" to B or if the
energy needed after the particle gets past the barrier is equal to or less
than A.

In quantum mechanics, there is a probability that the particle will pass
the barrier even if A is less than B. The closer A is to B, and the
shorter the time that the particle needs the higher energy to pass, the
higher the probability is that the particle will get past. The effect is
called tunneling.

--
Steve Gray

Steven Gray wrote:
"DARTH VADER" wrote in
oups.com:

What exactly is electron tunelling?

In classical physics, if a particle has energy A and it needs energy B to
get past a barrier, and A is less than B, then the particle simply won't
get past the barrier. This is true even if A is "close" to B or if the
energy needed after the particle gets past the barrier is equal to or less
than A.

In quantum mechanics, there is a probability that the particle will pass
the barrier even if A is less than B. The closer A is to B, and the
shorter the time that the particle needs the higher energy to pass, the
higher the probability is that the particle will get past. The effect is
called tunneling.

You can't say the particle goes through anything unless you apply
position measurements on it - when you do, you will find it follows the
classical predictions. That it "seems" to have "non-zero probability of
going through" arises from the inability to KNOW how it is moving
during the period that it is not being measured. If you don't look at
the particles then don't say it DID something, if you look then you can
say.

Just because you can observe a particle beyond the barrier does not
mean that it "went through" that barrier. It could've easily gone up
then done a few loops, then a few zig-zags, then gone back a bit, then
gone around the barrier and right into the detector. In fact there are
infinite paths if may have taken - the probability of each is the
absolute square of amplitude with Lagrangian time integral complex
phase. After you detect it you can start to deduce the classical path
it must necessarily have taken to have gotten there.



--
Steve Gray

what is shelfish?