Evanescent wave / tunneling

However, this is not a physically realizable solution since it would go to infinity at infinity. To obtain a physically realizable wavefunction, one must use boundary conditions to determine the amplitude of the wavefunction at the barrier. This results in a wavefunction that decays exponentially but does not go to infinity, making it an evanescent wave. In summary, the wavefunction within a rectangular potential barrier is an evanescent wave that decays exponentially away from the barrier and is obtained by using boundary conditions to determine the amplitude of the wavefunction at the barrier.
  • #1
jaejoon89
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How is the wavefunction within a rectangular potential barrier an evanescent wave?

I thought an evanescent wave was exponentially decaying. If you take x->infinity for the following function for E<V, one of the terms goes to 0 but the other term goes to infinity, so the wavefunction will go to infinity. Thus, it isn't physically realizable. But how you get the physically realizable wavefunction for E<V, what does it look like, and how is it an evanescent wave?

http://en.wikipedia.org/wiki/Schrödinger_equation#Time_independent_equation
 
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  • #2
_in_one_dimensionThe wavefunction within a rectangular potential barrier is an evanescent wave because the wavefunction decays exponentially away from the barrier. This behavior can be seen in the solution to the Schrödinger equation for a one-dimensional energy-independent potential, which has two components: a propagating wave and an exponentially decaying evanescent wave. For energies less than the potential barrier, only the decaying evanescent wave is present. This means that the wavefunction is exponentially decreasing away from the barrier.
 

Related to Evanescent wave / tunneling

1. What is an evanescent wave?

An evanescent wave is an electromagnetic wave that has a very short wavelength and decays rapidly as it travels through a medium. It is created when a wave of higher frequency hits the interface between two materials with different refractive indexes at an angle greater than the critical angle.

2. How does tunneling occur in an evanescent wave?

Tunneling is the phenomenon where an evanescent wave is able to penetrate through a barrier that it would not be able to pass through based on classical wave behavior. This occurs due to the quantum mechanical nature of the evanescent wave, which allows it to "tunnel" through the barrier and continue propagating on the other side.

3. What are the applications of evanescent waves and tunneling?

Evanescent waves and tunneling have numerous applications in various fields such as microscopy, optical sensing, and telecommunications. They are also used in technologies such as scanning tunneling microscopy, which allows for the imaging of individual atoms on a surface.

4. How are evanescent waves and tunneling related to the concept of total internal reflection?

Total internal reflection is the phenomenon where a wave is completely reflected at the interface between two materials due to the angle of incidence being greater than the critical angle. Evanescent waves and tunneling occur when the incident wave is at an angle greater than the critical angle, but some of the wave is able to pass through the interface due to its quantum mechanical nature.

5. Can evanescent waves and tunneling be observed in everyday life?

While evanescent waves and tunneling are not directly observable in everyday life, their effects can be seen in various technologies such as fiber optic communications and touch screens. They also play a crucial role in natural processes such as photosynthesis, where light is able to penetrate through the surface layers of leaves due to evanescent waves and tunneling.

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