Infinite potential well- Delta potential inside

In summary, the speaker is trying to find the odd solution to a potential well problem with a delta potential in the middle. They mention that they know odd solutions vanish for x=0 and are looking for a "normal potential well." They also mention that in the solution, they found the same result for n=1,2,3,4... instead of the expected even n's. They are also trying to find the even states and mention the difference between sine and cosine solutions. They ask for help from the others in the conversation.
  • #1
noamriemer
50
0
Hello again. Thank you guys. You have been great help...

I have another one:

Given a potential well- 2a is it's width, and in the middle - there is a delta potential:

[itex] V(x)= \frac {\hbar^2} {2m} \frac {\lambda} {a} \delta(x) [/itex]

I am looking for the odd solution to this problem.

I thought I should answer:
I know odd solutions vanish for x=0. Therefore, [itex] \psi'(0)=0 [/itex]
So I am looking at a "normal potential well": [itex] \varphi_n=\frac {1} {\sqrt a} sin(\frac {\pi nx} {2a} ) [/itex] for n=0,2,4,...

But in the solution- they got the same result, only for n=1,2,3,4,...
Why is that so? in the general solution for infinite well, the sin refers to the even n's...

Later on, I want to find the even states...
So I was trying to find a cosine based solution ... and I saw that again, in the solution, they were looking for a sine solution...
Why?

I think I am mixing things here, but as far as I understood- sine refers to the anti-symmetrical states, and to even n's, and the cosine - to symmetrical states and odd n's...
Thank you sooooo much!
Noam
 
Physics news on Phys.org
  • #2
Why don't you try starting from the Schrodinger equation... plug in the given potential, and try a solution of the form [itex] \psi(x) = A e^{\lambda x} [/itex].
 

FAQ: Infinite potential well- Delta potential inside

1. What is an infinite potential well?

An infinite potential well is a theoretical construct used in quantum mechanics to describe a particle confined to a certain region with an infinitely high potential barrier on all sides. This allows for the study of the particle's behavior and properties within this well.

2. How does the delta potential inside an infinite potential well affect a particle?

The delta potential inside an infinite potential well is a localized potential that creates a "spike" in the potential energy at a certain point within the well. This can affect the particle's energy levels and wavefunction, leading to interesting quantum effects.

3. What is the significance of the delta potential inside an infinite potential well in quantum mechanics?

The delta potential inside an infinite potential well serves as a simplified model for real-world systems with localized potential variations. By studying and understanding the behavior of particles in this simple system, we can gain insights into more complex systems in quantum mechanics.

4. How is the behavior of a particle affected by the width and depth of the delta potential inside an infinite potential well?

The behavior of a particle is highly dependent on the width and depth of the delta potential inside the infinite potential well. A deeper and narrower potential will result in a more localized and higher energy state for the particle, while a wider and shallower potential will lead to a more spread out and lower energy state.

5. Can the delta potential inside an infinite potential well be used to model real-world systems?

While the delta potential inside an infinite potential well has been proven to be a useful model in quantum mechanics, it is important to note that it is an idealized system and may not accurately represent all real-world systems. It is a useful tool for understanding and studying quantum phenomena, but caution should be exercised when applying it to real-world situations.

Back
Top