Quantum mechanics potential well solutions-help

In summary, the conversation is about finding the values of the unknown coefficients A, B, C, D, and F in the potential well barrier equation. The suggestion is to eliminate one coefficient at a time by substituting equations into each other until there is only one equation left for two of the coefficients, which can then be solved for (A/B)^2. This process requires a lot of algebra.
  • #1
asj23
1
0
I was working through the textbook and it just gave the solutions to the potential well barrier as in [B/A]*2 and [F/A]*2 and T i was trying to figure it out with the conditions but couldn't get the answer i have attached the conditions, can some one show me how to find these values from the conditions

thanks
Andrew
 

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  • #2
Show us what you've tried so far and maybe someone will be able to get you unstuck.

The basic idea is to eliminate the coefficients one at a time. You have four equations for five unknown coefficients A, B, C, D, F. First, you eliminate one coefficient by substituting equations into each other until you end up with three equations for four unknown coefficients. Then you eliminate another coefficient to get two equations for three unknown coefficients. Finally you get to one equation for, say, A and B, and that gives you [itex](A/B)^2[/itex].

Then you backtrack and find the other coefficients. It takes a lot of algebra!
 

1. What is a potential well in quantum mechanics?

A potential well in quantum mechanics is a region in space where a particle is confined due to a potential energy barrier. This can occur when the particle's kinetic energy is lower than the potential energy in the surrounding area, causing it to be trapped in the well.

2. How does solving for potential well solutions in quantum mechanics help us understand the behavior of particles?

By solving for potential well solutions, we can determine the allowed energy states and wave functions of particles within the well. This allows us to predict their behavior and interactions with other particles, providing insight into the fundamental principles of quantum mechanics.

3. What are the different types of potential wells in quantum mechanics?

There are three main types of potential wells: infinite, finite, and harmonic. Infinite potential wells have impenetrable barriers, while finite potential wells have barriers that particles can tunnel through. Harmonic potential wells have a parabolic shape and are used to model the behavior of atoms and molecules.

4. How do we solve for potential well solutions in quantum mechanics?

To solve for potential well solutions, we use the Schrödinger equation, which describes the behavior of quantum particles. The equation is solved using mathematical techniques such as separation of variables and boundary conditions, resulting in a set of allowed energy states and corresponding wave functions for the particle in the potential well.

5. What are some real-world applications of potential well solutions in quantum mechanics?

Potential well solutions have numerous applications in fields such as materials science, electronics, and quantum computing. They help us understand the behavior of electrons in semiconductors and the properties of materials at the nanoscale. They also play a crucial role in the design and development of quantum devices and technologies.

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