Quantm tunneling

  • #1
cyleung_2001
4
0
Can the phenomenon of quantum tunneling be explained? Any theory that can account for it? Or is it just empirical? Would someone kindly answer my questions? o:)
 
Last edited:

Answers and Replies

  • #2
Actually, tunneling is embodied completely in the Schrodinger equation.

Suppose you have a potential that is continuous everywhere (for simplicity. It need not be continuous, just so long as it remains finite for any finite point). Classically, in a conservative system, if the energy of your particle is less than the potential energy, the particle will never be found there. It's a "classically forbidden" area.

Now, in quantum mechanics, for various mathematical as well as physical reasons, the wave function for a particle must be continuous for such potentials, and therefore you get a particle that "leaks" into the classically forbidden area. In fact, if you have an INFINITE potential of finite length separating two areas (experimentally this would be approximated by, for example, an enormous electric field that is confined spacially), there is a nonzero chance that the particle will pop through that potential and end up on the other side. In the case of free particles with a potential, the decay is exponential, so as the distances grow large the probability drops, but tunneling is perfectly accounted for in conventional quantum mechanics.
 
  • #3
seratend
318
1
MalleusScientiarum said:
In fact, if you have an INFINITE potential of finite length separating two areas ... there is a nonzero chance that the particle will pop through that potential and end up on the other side.

Are you sure? really sure?

Seratend.
 
  • #4
Doc Al
Mentor
45,433
1,886
MalleusScientiarum said:
In fact, if you have an INFINITE potential of finite length separating two areas (experimentally this would be approximated by, for example, an enormous electric field that is confined spacially), there is a nonzero chance that the particle will pop through that potential and end up on the other side.
For an infinite potential barrier of finite width, the transmission coefficient is zero. (However if the infinite barrier is infinitely narrow--that is, a delta-function potential--that's a different story.)

... but tunneling is perfectly accounted for in conventional quantum mechanics.
Absolutely.
 
  • #5
selfAdjoint
Staff Emeritus
Gold Member
Dearly Missed
6,881
10
Believe it.
 
  • #6
cyleung_2001
4
0
I understand now. It'd be rather simple to visualize it by considering the wave function of a quantum harmonic oscillator.
 
  • #7
Oh yes...you're right...because the wave function goes as [tex]\sim e^{-V}[/tex] more or less. My bad.
 
Last edited by a moderator:

Suggested for: Quantm tunneling

  • Last Post
Replies
4
Views
245
  • Last Post
Replies
3
Views
327
Replies
14
Views
603
Replies
6
Views
368
  • Last Post
Replies
4
Views
537
  • Last Post
Replies
9
Views
819
  • Last Post
Replies
0
Views
509
Replies
2
Views
500
Replies
3
Views
451
Replies
2
Views
582
Top