Infinite potential well with Delta function inside

In summary, the conversation discusses a problem in quantum mechanics involving an infinite potential well with a delta potential. The question is raised about the effect of the delta potential on the energy levels and the value of λ that would result in a ground state energy of zero. The conversation also suggests finding a solution by looking at the energy eigenstates and applying additional boundary conditions. The end goal is to compare the energy spectrum to that of a normal infinite potential well.
  • #1
Ace10
17
0
Hello guys,

I need some serious help for the solution of a problem in Q.M, I'm not so sure if I deal with it properly..

Consider an infinite potential well with the traits:

V(x):∞, for x>a and x<-a

V(x):λδ(x), for -a≤x≤a

What happens to the energy levels due to the existence of the delta-potential and what is the value of λ so the ground state energy is zero?

I think that due to the delta potential if λ>0 the energy spectrum has increased values..

Can anybody think about it and untangle me? I would be grateful.

Thanks in advance:smile:
 
Physics news on Phys.org
  • #2
First you should find out how to solve the energy eigenstates for the normal delta function potential, read these:

http://en.wikipedia.org/wiki/Delta_potential
http://quantummechanics.ucsd.edu/ph130a/130_notes/node154.html

Next you solve the same problem, but with the additional boundary condition that the wave function must vanish at the boundaries of the infinite potential well: ##\psi(a)=\psi(-a)=0##. This additional constraint makes the energy spectrum discrete. Finally, compare the energy spectrum to that of the normal infinite potential well.
 

FAQ: Infinite potential well with Delta function inside

1. What is an infinite potential well with a Delta function inside?

An infinite potential well with a Delta function inside is a theoretical model used in quantum mechanics to describe the behavior of a particle confined within a potential well. In this model, the potential well has infinite walls and a Delta function, which represents a localized potential, at a specific position within the well.

2. What is the significance of a Delta function in this model?

The Delta function represents a very narrow and high potential barrier within the infinite potential well. This barrier causes the particle to behave differently than if the potential well were simply infinite on both sides. It can lead to interesting quantum effects such as tunneling and resonant states.

3. How does the position of the Delta function affect the energy levels of the particle?

The position of the Delta function within the potential well can greatly affect the energy levels of the particle. If the Delta function is located in the middle of the well, it can create a symmetric potential, leading to even energy levels. However, if the Delta function is located off-center, it can create an asymmetric potential, resulting in uneven energy levels.

4. Can the Delta function be moved within the potential well?

Yes, the Delta function can be moved within the potential well. This can be done by changing the parameters of the potential well, such as its width or depth. Moving the Delta function can alter the energy levels and behavior of the particle, providing a way to manipulate the system in this model.

5. How is the infinite potential well with a Delta function inside different from a regular infinite potential well?

The addition of a Delta function inside the potential well adds complexity to the system. It introduces a localized potential that can lead to quantum effects such as tunneling and resonant states. In contrast, a regular infinite potential well does not have any potential barriers within it, resulting in simpler energy levels and behavior for the particle.

Similar threads

Wave function of infinite potential well
Replies
19
Views
1K
Average value of the impulse as the parameters vary
Replies
14
Views
2K
Double Delta Potential: Solving Particle Scattering Problem
Replies
12
Views
2K
What is the number of confined states in these potential wells?
Replies
3
Views
1K
Harmonic potential exercise with perturbation theory
Replies
2
Views
858
Infinite Square Well, Potential Barrier and Tunneling
Replies
1
Views
3K
Probability of finding a particle in the right half of a rectangular potential well
Replies
16
Views
2K
Energy Difference with a Two Delta Function Potential
Replies
16
Views
2K
Infinite potential well with delta well
Replies
9
Views
3K
Given the potential find the eigenfunction
Replies
10
Views
962

Hot Threads

Recent Insights

Back
Top