Reflected and Transmitted wavefunction (QM)

In summary, the reflected wavefunction is the portion of a wavefunction that bounces off a potential barrier or interface, while the transmitted wavefunction is the portion that passes through it. They are related by the reflection and transmission coefficients, and there is always a non-zero probability of both reflection and transmission, even for high barriers. The energy of the incident particle affects the wavefunctions through the relationship between energy and momentum, with higher energy particles having a higher probability of transmission. The behavior of the wavefunctions is also influenced by the shape and height of the barrier or interface, as well as the properties of the incident particle.
  • #1
Noctisdark
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35

Homework Statement


I'm asked to calculate the reflected and transmitted part of the wavefunction, in fact, this is the first time i encounter this so i need your assistance.

Homework Equations


Time independant schrodinger equation + continuity condition

The Attempt at a Solution


See the pic[/B]
 

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  • #2
Hi Noctisdark, could you please upload a picture where your attempt is easier to see? It is quite difficult to understand what you are trying to do on such a dark and poor resolution photo.
 

1. What is the difference between reflected and transmitted wavefunction in quantum mechanics?

The reflected wavefunction refers to the portion of the wavefunction that bounces off a potential barrier or interface, while the transmitted wavefunction is the portion that passes through the barrier or interface.

2. How are the reflected and transmitted wavefunctions related to each other?

The reflected and transmitted wavefunctions are related by the reflection and transmission coefficients, which describe the probability of reflection and transmission, respectively.

3. Can the wavefunction be completely reflected or transmitted?

In quantum mechanics, there is always a non-zero probability of both reflection and transmission, even if the barrier or interface is very high. However, the probability of complete reflection or transmission can be very small.

4. How does the energy of the incident particle affect the reflected and transmitted wavefunctions?

The energy of the incident particle affects the reflected and transmitted wavefunctions through the relationship between energy and momentum in quantum mechanics. Higher energy particles have a greater momentum and thus a higher probability of transmission through a potential barrier.

5. What factors influence the behavior of the reflected and transmitted wavefunctions?

The behavior of the reflected and transmitted wavefunctions is influenced by the shape and height of the potential barrier or interface, as well as the energy and properties of the incident particle, such as its mass and spin.

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