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What is the physics behind quantum tunneling

by einstein1921
Tags: physics, quantum, tunneling
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einstein1921
#1
Nov21-12, 07:58 AM
P: 73
Hi, My friends! According to quantum mechanics books ,a particle has some probability hop through the potential even when the potential is large than kinetic energy. They all explain the phenomenon by solving Schrodinger equation. Indeed, the wavefunction doesn't equal 0 behind the potential. But I want to know how the particle go through the potential? What is the physics behind quantum tunneling? I can't accept the explaination in books! Everyone who says something about quantum tunneling would be highly appreciated.
let us talk about it!!
best wishes!!
PS: I read something about STM. the book says that because of tunneling ,the electron of metal are not confined the inner of surface,that is to say ,electron density don't fall to zero at the surface,but attenuation exp(), I want to know why the electron leaves the metal ,and they have pass the potential barrier!!!
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DrewD
#2
Nov21-12, 08:13 AM
P: 445
The physics IS the Shrodinger Equation. There is a lot to think about, but there is no Classical explanation, which is what it sounds like you are looking for. I understand your ambivalence, but Nature does not care what you are willing to accept. The physics behind it is quantum mechanics which does not require localized particles as the system evolves. Sorry.
mycotheology
#3
Nov21-12, 04:35 PM
P: 90
I think its Heisenbergs uncertainty principle. The smaller a particle is, the less its position in space can be known. As a result, it exists in multiple locations in space.

Neandethal00
#4
Nov21-12, 06:59 PM
P: 168
What is the physics behind quantum tunneling

Quote Quote by DrewD View Post
The physics IS the Shrodinger Equation. There is a lot to think about, but there is no Classical explanation, which is what it sounds like you are looking for. I understand your ambivalence, but Nature does not care what you are willing to accept. The physics behind it is quantum mechanics which does not require localized particles as the system evolves. Sorry.
Can we say the particle tunnel through the barrier instantly or faster than c? We don't know how the particle behind the barrier suddenly appears in front of the barrier? Can it be another phenomena similar to quantum entanglement?
mfb
#5
Nov22-12, 08:29 AM
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Quote Quote by Neandethal00 View Post
Can we say the particle tunnel through the barrier instantly or faster than c?
No. Signal propagation speed is always limited by the speed of light. However, it is tricky to say "the particle is at this side right now" - to get the position very precise, the particle needs a large momentum uncertainty, which helps tunneling (and if its energy is large enough, it does not even have to tunnel).
ZapperZ
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Nov22-12, 09:11 AM
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Quote Quote by Neandethal00 View Post
Can we say the particle tunnel through the barrier instantly or faster than c? We don't know how the particle behind the barrier suddenly appears in front of the barrier? Can it be another phenomena similar to quantum entanglement?
No, you cannot say that. Try finding the momentum of the particle inside the barrier. It is not infinite.

Zz.
Neandethal00
#7
Nov22-12, 10:59 AM
P: 168
Quote Quote by ZapperZ View Post
No, you cannot say that. Try finding the momentum of the particle inside the barrier. It is not infinite.

Zz.
Yes, I remember it now.
Probability function drops sharply inside the barrier but never zero.

Then only physical explanation can be made this way:
The particle somehow interacts with the potential barrier.

In microscopic world this interaction is possible, but not in macroscopic world.
einstein1921
#8
Nov22-12, 07:41 PM
P: 73
Quote Quote by DrewD View Post
The physics IS the Shrodinger Equation. There is a lot to think about, but there is no Classical explanation, which is what it sounds like you are looking for. I understand your ambivalence, but Nature does not care what you are willing to accept. The physics behind it is quantum mechanics which does not require localized particles as the system evolves. Sorry.
you means that we can't think the particle as a localized dot, but a unlocalized something!!
einstein1921
#9
Nov22-12, 07:45 PM
P: 73
thank you all!!is this ture? when particle is confined in the barrier,according to Heisenberg's uncertainty principle, the momentum will become larger than the potential barrier,even though it doesn't large than the barrier at first!! so in essence, the particle's energy still is larger than the potential,so it can hop through the barrier!!
PS: the question is if particle's energy increases because of Heisenberg's uncertainty principle, what form of energy is decrease? energy conservation!!
Drakkith
#10
Nov22-12, 09:39 PM
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From wiki: http://en.wikipedia.org/wiki/Conserv...Quantum_theory

Quantum theory

In quantum mechanics, energy of a quantum system is described by a self-adjoint (Hermite) operator called Hamiltonian, which acts on the Hilbert space (or a space of wave functions ) of the system. If the Hamiltonian is a time independent operator, emergence probability of the measurement result does not change in time over the evolution of the system. Thus the expectation value of energy is also time independent. The local energy conservation in quantum field theory is ensured by the quantum Noether's theorem for energy-momentum tensor operator. Note that due to the lack of the (universal) time operator in quantum theory, the uncertainty relations for time and energy are not fundamental in contrast to the position momentum uncertainty principle, and merely holds in specific cases (See Uncertainty principle). Energy at each fixed time can be precisely measured in principle without any problem caused by the time energy uncertainty relations. Thus the conservation of energy in time is a well defined concept even in quantum mechanics.
derek101
#11
Nov23-12, 06:42 AM
P: 22
It's not that the particle has enough energy to get through the barrier,energy fluctuations in the barrier can push the particle through it(by absorbing and emitting).
Drakkith
#12
Nov23-12, 11:44 AM
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Quote Quote by derek101 View Post
It's not that the particle has enough energy to get through the barrier,energy fluctuations in the barrier can push the particle through it(by absorbing and emitting).
This is not correct. The particle itself is what has the uncertainty that allows it to appear on the other side of the barrier. Are you aware of what a "barrier" is? It doesn't have to be a physical barrier. For example, there is a barrier in Proton-Proton fusion in the Sun in the form of electromagnetic repulsion between the protons. They shouldn't have enough energy to fuse, as the repulsion is strong enough in a classical sense to keep them apart, however they protons can tunnel through this barrier and fuse. The barrier represents something that the particle couldn't normally do, whether it's tunnel through a repulsive force or out of an attractive one, as in the case of spontaneous nuclear fission.
derek101
#13
Nov23-12, 12:54 PM
P: 22
Drakkith
If it's the particle itself that has the uncertainty then:-
Are you saying that 2 protons in the vacuum of space,have the same chance of tunneling through the barrier,as 2 protons in the middle of the sun?
Bill_K
#14
Nov23-12, 01:37 PM
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Are you saying that 2 protons in the vacuum of space,have the same chance of tunneling through the barrier,as 2 protons in the middle of the sun?
Funny you should mention that. Our understanding of the nuclear processes that go on in the solar interior depends on making measurements on those same reactions in the lab. If the reaction rates were not the same in both environments, it would be painfully obvious.
Maui
#15
Nov23-12, 03:45 PM
P: 724
Quote Quote by einstein1921 View Post
Hi, My friends! According to quantum mechanics books ,a particle has some probability hop through the potential even when the potential is large than kinetic energy. They all explain the phenomenon by solving Schrodinger equation. Indeed, the wavefunction doesn't equal 0 behind the potential. But I want to know how the particle go through the potential? What is the physics behind quantum tunneling?

Well it certainly isn't classical physics. Someone mentioned the uncertainty principle and the different principles of quantum physics. The difficulty lies in accepting that atoms are more like processes and much less like rocks(i am still struggling as this must hold for larger objects too, but so was Heisenberg and everyone else):

"In modern physics, atoms lose this last property, they possess geometrical qualities in no higher degree than colour, taste, etc. The atom of modern physics can only be symbolized by a partial differential equation in an abstract multidimensional space. Only the experiment of an observer forces the atom to indicate a position, a colour and a quantity of heat. All the qualities of the atom of modern physics are derived, it has no immediate and direct physical properties at all, i.e. every type of visual conception we might wish to design is, eo ipso, faulty. An understanding of 'the first order' is, I would almost say by definition, impossible for the world of atoms"

— Werner Heisenberg

Philosophic Problems of Nuclear Science, trans. F. C. Hayes (1952), 38.
derek101
#16
Nov23-12, 07:21 PM
P: 22
If the the repulsive force between 2 protons,is mediated by the creation and exchange of virtual particles,and this field of virtual particles is the barrier,then you have just as much uncertainty about the position and strength of the barrier,as you do about the position and momentum of the protons.
ZapperZ
#17
Nov23-12, 07:35 PM
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Quote Quote by derek101 View Post
If the the repulsive force between 2 protons,is mediated by the creation and exchange of virtual particles,and this field of virtual particles is the barrier,then you have just as much uncertainty about the position and strength of the barrier,as you do about the position and momentum of the protons.
Can you show where in the various tunneling phenomena experiments, say the SIN tunneling spectroscopy using superconductors, that this barrier uncertainty manifests its effect?

Zz.
Spinalcold
#18
Nov23-12, 11:14 PM
P: 17
One of my favorite quotes deals with the difficulty in understanding this.

Freeman Dyson: "Thirty-one years ago, Dick Feynman
told me about his "sum-over-histories" version of quantum
mechanics. "The electron does anything it likes", he said, "it goes
in any direction at any speed, forward or backward-in-time,
however it likes, and then you add-up the amplitudes and it gives
you the wave function." I said to him, "Your crazy". But he
wasn't."


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