# Quantum tunnelling for a finite-square potential parrier

• blaksheep423
In summary, a proton with a kinetic energy of 10 eV is traveling in the x direction and encounters a potential barrier of height 12 eV and width .2nm at x = 1nm. The potential returns to 0 at x = 1.2nm. The question asks for the probabilities of transmission (T) and reflection (R) after the collision, which can also be interpreted as the probabilities of finding the particle on either side of the barrier.
blaksheep423

## Homework Statement

At x=0, a proton with a kinetic energy of 10 eV is traveling in the x direction (potential energy = 0). At x = 1nm, it encounters a potential barrier of height 12 eV and width .2nm. The potential returns to 0 at x = 1.2nm.

Give the amount of the particle on both sides of the barrier after the collision.

## Homework Equations

T - Probability of Transmission
R - Probability of Reflection

## The Attempt at a Solution

Actually my question here isn't about the exact solution. Does anyone know what is meant by "the amount of the particle on both sides"? is this just another way of asking for T and R?

"amount of the particle on both sides" doesn't really make sense, but I guess it's supposed to mean T and R - the late-time probabilities of the particle being found on either side of the barrier. I can't think of anything else interesting that you could be expected to find.

## 1. What is quantum tunnelling for a finite-square potential barrier?

Quantum tunnelling is a phenomenon in quantum mechanics where a particle can pass through a potential barrier even if it does not have enough energy to overcome the barrier. This is possible due to the wave-like nature of particles, which allows them to exist in multiple places at once. In the case of a finite-square potential barrier, the barrier has a finite height and width, and the particle can tunnel through it if its energy is within a certain range.

## 2. Why is quantum tunnelling for a finite-square potential barrier important?

Quantum tunnelling is important because it plays a crucial role in various physical processes, such as nuclear fusion, radioactive decay, and electron transport in semiconductors. It also has applications in technologies like scanning tunneling microscopy and tunnel diodes.

## 3. How does the probability of quantum tunnelling change with barrier height and width?

The probability of quantum tunnelling decreases with increasing barrier height and width. This is because a higher and wider barrier requires more energy for the particle to tunnel through it, and the probability of the particle having enough energy decreases with increasing barrier parameters.

## 4. Can quantum tunnelling occur for particles with any energy?

Yes, quantum tunnelling can occur for particles with any energy. However, the probability of tunnelling decreases as the energy of the particle increases. This is because higher energy particles are less likely to be confined to a smaller region, making it more difficult for them to tunnel through the potential barrier.

## 5. How is quantum tunnelling for a finite-square potential barrier affected by the shape of the barrier?

The shape of the potential barrier can affect the probability of quantum tunnelling. A smooth and gradual barrier will have a higher probability of tunnelling compared to a sharp and steep barrier. This is because a gradual barrier allows for a smoother transition of the wave function, making it easier for the particle to tunnel through.

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