Quantum Tunneling: Explained, Theories & Answers

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In summary, the phenomenon of quantum tunneling can be explained through the Schrodinger equation, which accounts for particles leaking into classically forbidden areas due to the continuity of the wave function. Even in the case of an infinite potential barrier of finite width, there is still a chance for the particle to tunnel through. This is perfectly accounted for in conventional quantum mechanics.
  • #1
cyleung_2001
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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:)
 
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  • #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
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
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
Believe it.
 
  • #6
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.
 
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1. What is quantum tunneling?

Quantum tunneling is a phenomenon in quantum mechanics where a particle can pass through a potential barrier even though it does not have enough energy to do so classically.

2. How does quantum tunneling occur?

Quantum tunneling occurs due to the probabilistic nature of quantum mechanics. In quantum mechanics, particles do not have a well-defined position or momentum. Instead, they exist as a probability distribution. This allows for the possibility of particles to exist on the other side of a potential barrier.

3. What are some real-life examples of quantum tunneling?

Quantum tunneling is a fundamental process in several natural phenomena, such as nuclear fusion in stars and radioactive decay. It also plays a crucial role in modern technology, such as in the operation of transistors in electronic devices.

4. What is the significance of quantum tunneling in quantum computing?

In quantum computing, quantum tunneling is utilized to perform operations on qubits, which are the building blocks of quantum computers. It allows for the manipulation of the quantum state of a system, which is essential for performing quantum computations.

5. Are there any theories that explain quantum tunneling?

Yes, there are several theories that attempt to explain quantum tunneling, such as the Schrödinger equation, Heisenberg's uncertainty principle, and the Copenhagen interpretation. However, there is still ongoing research and debate in the scientific community about the exact nature of quantum tunneling.

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