Quantum tunneling probability density

In summary, when an electron tunnels through a potential barrier, its wavefunction is described by a plane wave traveling in the positive x direction. In this region, the probability density is constant and is expressed by multiplying the wavefunction by its complex conjugate. This is a positive energy solution to the Schrodinger equation with no potential. However, the reason for the constant probability density is still unclear and cannot be found in books or on the internet.
  • #1
swain1
30
0

Homework Statement


When an electron has tunnelled through a potential barrier it's wavefunction is described by a plane wave traveling in the positive x direction. In this region the probability density is constant. I am trying to explain why it is constant but can't find any info in books or on the internet.


Homework Equations


f(x)=Fexp(ikx)


The Attempt at a Solution



Have had some ideas which haven't worked out to be right. I now it is something to do with the wavefunction being a plane wave but can't work out why it is constant.
 
Physics news on Phys.org
  • #2
How is probability density expressed in terms of a wavefunction?
 
  • #3
It's a positive energy solution to the schrodinger equation with no potential. So as you say it's proportional to exp(ikx). To get probability density you take that times it's complex conjugate. What do you get?
 

1. What is quantum tunneling probability density?

Quantum tunneling probability density is a concept in quantum mechanics where a particle has a probability of appearing on the other side of a barrier, even though it does not have enough energy to overcome the barrier. This phenomenon arises due to the probabilistic nature of particles at the quantum level.

2. How is quantum tunneling probability density calculated?

The calculation of quantum tunneling probability density involves using the Schrödinger equation and the wave function of the particle. The wave function describes the probability amplitude of the particle at different points in space and time. By solving the Schrödinger equation, the probability density can be determined at any given point.

3. What factors affect the probability of quantum tunneling?

The probability of quantum tunneling is affected by the height and width of the barrier, the energy of the particle, and the mass of the particle. A higher barrier or a lower energy particle will result in a lower probability of tunneling, while a narrower barrier or a lighter particle will result in a higher probability of tunneling.

4. What is the significance of quantum tunneling probability density?

Quantum tunneling probability density has significant implications in various fields such as solid-state physics, chemistry, and nuclear physics. It helps explain phenomena such as alpha decay, nuclear fusion, and the operation of tunnel diodes. It also plays a crucial role in the development of technologies such as scanning tunneling microscopes and quantum computers.

5. Can quantum tunneling be observed in everyday life?

Yes, quantum tunneling can be observed in everyday life. For example, it is the mechanism behind the operation of tunnel diodes, which are used in electronic devices such as computers and cell phones. It is also a crucial process in nuclear fusion, which powers the sun and other stars. However, it is not observable in macroscopic objects due to their large mass and low probability of tunneling.

Similar threads

  • Advanced Physics Homework Help
Replies
1
Views
1K
Replies
2
Views
853
Replies
7
Views
938
  • Quantum Physics
Replies
1
Views
733
  • Advanced Physics Homework Help
Replies
3
Views
1K
  • Quantum Physics
Replies
13
Views
2K
  • Advanced Physics Homework Help
Replies
3
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
965
  • Advanced Physics Homework Help
Replies
1
Views
3K
  • Quantum Physics
Replies
3
Views
1K
Back
Top