Finite Square Well: Bond States and Asymmetric Potential Wells

In summary, the conversation discusses the existence of bound states in an asymmetric potential well compared to a symmetric one. The speaker is unsure how it is possible for the asymmetric potential well to not have bound states if the energy is less than the barrier heights, while the symmetric case always has a solution. They also mention that an explicit equation for bound states in the asymmetric potential well is not difficult to derive, and at least one bound state can be found from this equation.
  • #1
LagrangeEuler
717
20
I am not sure how is it possible that asymetric potential well does not have bond states if ##E<U_1<U_2##. In symmetric case solution always exists. Why this is a case?
 
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  • #2
LagrangeEuler said:
I am not sure how is it possible that asymetric potential well does not have bond states if ##E<U_1<U_2##. In symmetric case solution always exists. Why this is a case?
I may be misunderstanding the question here... The asymmetric finite square well does have bound state solutions.
 
  • #3
But not always. Right? Symmetric square well always has bound state solution.
 
  • #4
For square (asymmetric) potential well an explicit equation with respect to energies of bound states is not difficult to derive. The existence of at least one bound state follows from that equation almost immediately.
 

1. What is a finite square well?

A finite square well is a potential energy function commonly used to represent a particle trapped within a specific region. It has a finite width and is typically symmetrical, meaning the potential energy is equal on both sides of the well.

2. What are bond states in a finite square well?

Bond states are the energy levels that a particle can occupy within a finite square well. These states correspond to the allowed energy levels of the particle as it moves within the well.

3. How does the depth of a finite square well affect the bond states?

The depth of a finite square well directly affects the energy levels or bond states that a particle can occupy within the well. A deeper well will have more bond states and a shallower well will have fewer bond states.

4. What is an asymmetric potential well?

An asymmetric potential well is a type of finite square well where the potential energy on one side is different from the other. This results in an uneven distribution of bond states and can significantly impact the behavior of particles within the well.

5. How are finite square wells used in real-world applications?

Finite square wells are used in a variety of real-world applications, including modeling electron behavior in atoms, studying quantum tunneling, and analyzing potential energy barriers in chemical reactions. They are also used in the design of microelectronic devices such as quantum wells and quantum dots.

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