# How Does Quantum Tunneling Affect Electron Reflection Probability?

• PsychonautQQ
In summary, an electron encountering a step with a potential drop of 2 eV will have a reflection probability of 50%.
PsychonautQQ

## Homework Statement

Calculate the reflection probability for a 5 eV electron encountering a step in which the potential drops by 2 eV

## The Attempt at a Solution

To answer this question, wouldn't I need to know where E > U or U > E? Also wouldn't I need to know the width of the potential barrier it's trying to penetrate?

The way I understand the question is as follows:

Take the potential function
$$V(x) = \left\{ \begin{array}{ll} 0 & x \le 0 \\ - 2\text{ eV} & x > 0 \end{array} \right.$$
and consider an electron coming in from ##x = -\infty## with an energy of 5 eV.

PsychonautQQ said:

## Homework Statement

Calculate the reflection probability for a 5 eV electron encountering a step in which the potential drops by 2 eV

## The Attempt at a Solution

To answer this question, wouldn't I need to know where E > U or U > E? Also wouldn't I need to know the width of the potential barrier it's trying to penetrate?

From what you say,I see that you haven't understood the question,and so you can't get the answer.
An important point that seems you don't know,is that only potential energy difference has physical significance.So you can choose where the potential is zero arbitrarily and so a constant potential can always be called zero.The problem is saying that an electron is moving in a constant potential till it reaches a potential drop.So we can call the potential before the potential drop to be zero and negative after that.Also because no other change in potential is stated,we can assume that the potential is constant till it drops somewhere and then stays constant again and so there is no width.Also its not a potential barrier,you can call it a potential canyon,starting at the point of drop and continuing till infinity.

## What is quantum tunneling?

Quantum tunneling is a phenomenon in which a particle can pass through a potential barrier that it classically does not have enough energy to overcome. This occurs due to the wave-like nature of particles at the quantum level.

## What is the significance of quantum tunneling?

Quantum tunneling is a fundamental process in quantum mechanics and has various applications in fields such as electronics, nuclear physics, and chemistry. It also plays a crucial role in explaining radioactive decay and fusion reactions.

## How does quantum tunneling occur?

Quantum tunneling occurs when a particle's wave function extends into a potential barrier, allowing it to have a probability of being found on the other side. This probability decreases exponentially with the width and height of the barrier.

## What factors affect the probability of quantum tunneling?

The probability of quantum tunneling is affected by the width and height of the potential barrier, as well as the mass and energy of the particle. Higher barriers and lower particle energies decrease the probability of tunneling.

## Can quantum tunneling be observed in everyday life?

While quantum tunneling is a fundamental process, it is usually only observable on the atomic or subatomic level. However, some macroscopic systems, such as superconductors and Josephson junctions, can exhibit quantum tunneling effects at extremely low temperatures.

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