Bound state of finite square well, why do we make this statement?

In summary, this conversation discusses a scattering problem with a beam of particles coming in from one side and some of them being reflected by a potential well. The reflected wave represents the particles bouncing back from the well. In a bound state, there is no incident wave and thus no reflected or transmitted wave. The exponential decay in the wavefunction outside the well indicates a small probability of finding the particle outside the potential well. This is due to the solution of the time-independent Schrödinger equation and the relationship between wavefunctions and the probability of finding a particle at a certain position.
  • #1
Outrageous
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Reading from http://quantummechanics.ucsd.edu/ph130a/130_notes/node150.html
Again we have assumed a beam of definite momentum incident from the left and no wave incident from the right.

Why is the above statement made?
What does the reflected wave mean? There is now all why reflected?
Please guide .thanks
 
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  • #2
This is not a bound state problem, which would have E < 0. It is a scattering problem, which has E > 0. We assume that we have a wave coming in from one side, corresponding to a beam of particles coming in from that side. We assume they are coming in from only one side, for simplicity.

What does the reflected wave mean?

It means that some of the particles "bounce back" from the well instead of passing through.

There is now all why reflected?

I'm sorry, I don't understand this question. :confused:
 
  • #3
jtbell said:
This is not a bound state problem, which would have E < 0. It is a scattering problem, which has E > 0. We assume that we have a wave coming in from one side, corresponding to a beam of particles coming in from that side. We assume they are coming in from only one side, for simplicity.



It means that some of the particles "bounce back" from the well instead of passing through.

I'm sorry, I don't understand this question. :confused:
Thanks
Yup, it is scattering state. So it doesn't mean we don't have wave from the right, we take only left for simplicity.
Reflected means bounce back, but in this scattering state, there is no potential wall or any wall, why the wave bounce back?
 
  • #4
One more to ask, for bound state, do we still have wave transmitted and reflected? No enough energy to transmit? What is the negative energy mean?
 
  • #5
Outrageous said:
Reflected means bounce back, but in this scattering state, there is no potential wall or any wall, why the wave bounce back?
Just like a part of the wave gets transmitted through a potential wall, a part of the wave is reflected by a potential well. Classical intuition fails here.

Outrageous said:
One more to ask, for bound state, do we still have wave transmitted and reflected?
The wavefunction of a bound state shows an exponential decay outside the well. There are no incident waves and thus neither a transmitted nor a reflected wave.
 
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  • #6
kith said:
Just like a part of the wave gets transmitted through a potential wall, a part of the wave is reflected by a potential well. Classical intuition fails here.

Actually no, it doesn't. Classical waves can reflect off wells or dips in a very similar way. For example, the sound waves inside a tube of a wind instrument (like a flute) partially reflect off an open end of the tube.
 
  • #7
You are right. What fails is the classical intuition about particles.
 
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  • #8
kith said:
The wavefunction of a bound state shows an exponential decay outside the well. There are no incident waves and thus neither a transmitted nor a reflected wave.

Why there is no incident wave ,yet we still have exponential function?
 
  • #9
Why do you think there is a problem with that?
 
  • #10
jtbell said:
Why do you think there is a problem with that?
The exponential function ( is not complex ) here doesn't represent wave that is why no wave outside the well.
But why do we have exponential function outside the well? What does it represent?
 
  • #11
Outrageous said:
But why do we have exponential function outside the well? What does it represent?
We have it because it appears in the solution of the time-independent Schrödinger equation. Like the other wavefunctions, it is related to the probability to find the particle at a certain position. So the exponential decay indicates that there's also a small probability to finde the particle outside the potential well although it is in a bound state. You can see a visualization of the solutions here
 
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FAQ: Bound state of finite square well, why do we make this statement?

1. What is a bound state in the context of a finite square well?

A bound state refers to a state in which a particle is confined within a finite potential well. In the case of a finite square well, the particle is bound within the boundaries of the well due to the potential energy barrier created by the well walls.

2. Why do we specifically use the term "finite" square well?

The term "finite" refers to the fact that the potential well has finite boundaries, as opposed to an infinite potential well which has no boundaries. In the context of a finite square well, this means that the particle is confined within a specific region and cannot escape beyond the boundaries of the well.

3. What is the significance of the finite square well in quantum mechanics?

The finite square well is a commonly used model in quantum mechanics to represent a particle confined within a finite region. It allows for the study of energy states and wave functions in a confined system, which has applications in understanding various physical phenomena such as electron behavior in atoms and nuclei.

4. How do we determine the bound states of a finite square well?

The bound states of a finite square well can be determined by solving the Schrödinger equation for the given potential well. This involves finding the energy eigenvalues and corresponding wave functions that satisfy the boundary conditions of the well. The number of bound states is determined by the depth and width of the well.

5. What is the physical interpretation of the bound states in a finite square well?

The bound states in a finite square well represent the discrete energy levels that a particle can have within the well. These energy levels correspond to the particle being confined within the well and are a result of the potential energy barrier created by the well walls. The wave function of the particle describes the probability of finding the particle at a particular energy level within the well.

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