Understanding Scattering and Bound State Solutions in Quantum Mechanics

In summary, the conversation discusses the concept of scattering states and bound states in quantum mechanics. It is noted that scattering states always have an imaginary wave function, but bound states can also have an imaginary wave function. The conversation also brings up Griffiths' use of sine/cosine functions instead of exponentials in some cases and the benefits of exploiting even/odd solutions.
  • #1
Logan Rudd
15
0
1)So from my understanding, as long as ##E>0## you will have scattering states and these scattering states will always result in an imaginary ##\psi##, but bound states can also have an imaginary ##\psi##? Is this correct and or is there a better way of looking at this maybe more conceptually?

2)I noticed in a footnote in griffiths intro to qm 2nd ed. in the finite square well section he mentions that he wrote ##\psi## in terms of sin/cos instead of exponentials because we know the solutions will be even or odd because the potential is symetric. But he also does it for the infinite square well when it's not really symmetric (at least with respect to the y-axis) and doesn't do it for the delta potential. How come he doesn't do it for the delta potential, is it not really symmetric? and why does he do it for the finite square well?
What is the benefit of "exploiting the even/odd solutions" and what does he mean by that?

Thanks
 
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  • #2
Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

What is scattering and how does it occur?

Scattering is a process in which particles interact with each other, causing a change in their trajectory or energy. This can occur through a variety of mechanisms, such as electromagnetic interactions, strong and weak nuclear forces, or gravitational interactions.

What are bound states and how do they differ from scattering states?

Bound states are states in which particles are confined to a specific region of space due to the presence of a potential barrier. In contrast, scattering states are states in which particles are not confined and can move freely. Bound states have discrete energy levels, while scattering states have continuous energy spectra.

What are some real-world applications of scattering and bound states?

Scattering and bound states have numerous real-world applications, including in particle accelerators, nuclear reactors, and medical imaging techniques such as X-ray and MRI. They are also important in understanding the properties of materials and developing new technologies.

How do scientists study scattering and bound states?

Scientists study scattering and bound states through a combination of theoretical calculations and experimental measurements. Theoretical models, such as quantum mechanics, are used to predict the behavior of particles in these states, while experiments involving particle accelerators, detectors, and other instruments are used to test these predictions and gather data.

What are some current research topics in scattering and bound states?

Current research in scattering and bound states includes studying the properties of exotic particles, understanding the behavior of matter at extreme temperatures and densities, and developing new materials with unique scattering and bound state properties for various applications.

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