How do I set up a delta potential well with an infinite potential wall?

In summary, the speaker is seeking help with solving a delta potential well with an infinite potential wall on one side and an open side a distance away. They provide a picture of their work so far and ask for guidance on how to set up the problem, wondering if it is a math or physics issue. They confirm that they are looking for a bound state with energy less than 0 and acknowledge that their solution format is correct. They also clarify their boundary conditions and express gratitude for the help.
  • #1
maverick_76
19
1
Okay so I am trying to solve a delta potential well with an infinite potential wall on one side a distance a away from the well. The other side is open so I am confused about how to set up the problem. Here is a picture of my work so far and if anyone has an insight into this I'd appreciate some guidance, thanks! My diff eq. is a little rusty so I'm wondering if my problem here is just math related or physics related, or both :p
 

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  • #2
A couple of questions for clarification. Are you looking for a bound state with energy < 0? If you are, the form of your solution is correct.
You have not explicitly stated your boundary conditions. The boundary condition for the wave function at x = 0 is: ψI(0) = 0. This will prove that A = -B, so you are correct.
 
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  • #3
Yes I am looking for the bound state of a particle. Awesome! Thank you!
 

FAQ: How do I set up a delta potential well with an infinite potential wall?

What is a Delta potential well problem?

A Delta potential well problem is a mathematical model used to describe the behavior of a particle in a one-dimensional potential well, where the potential energy is zero everywhere except at one point, where it is infinitely high. This point is known as the "delta function".

What is the significance of the Delta potential well problem?

The Delta potential well problem is significant because it allows us to study the behavior of particles in a confined space, which can help us understand the properties of quantum systems. It also has practical applications in solid-state physics and semiconductor devices.

How is the Delta potential well problem solved?

The Delta potential well problem is solved using mathematical techniques such as the Schrödinger equation and boundary conditions. The solution involves finding the eigenvalues and eigenfunctions of the system, which describe the energy levels and corresponding wave functions of the particle.

What are the applications of the Delta potential well problem?

The Delta potential well problem has applications in various fields such as quantum mechanics, solid-state physics, and semiconductor devices. It is also used in the study of quantum tunneling, which is important in understanding phenomena such as alpha decay and scanning tunneling microscopy.

What are the limitations of the Delta potential well problem?

One limitation of the Delta potential well problem is that it is a simplified model and does not take into account the complexities of real-world systems. It also assumes that the potential is constant within the well, which may not always be the case. Additionally, the problem is limited to one-dimensional systems, which may not accurately represent three-dimensional systems.

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