Bound State Wavefunctions vs Non-Bound State Wavefunctions

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SUMMARY

Bound state wavefunctions, represented by the equation e-kr/r, exhibit distinct characteristics compared to non-bound state wavefunctions, which are expressed as Sl(ikr)/r + e-ikr/r. The key difference lies in the behavior of these wavefunctions at large distances, where bound states do not have incoming waves, while non-bound states include a scattering amplitude term. Understanding this distinction is crucial for interpreting their graphical representations and physical implications in quantum mechanics.

PREREQUISITES
  • Quantum mechanics fundamentals
  • Wavefunction analysis
  • Understanding of scattering theory
  • Complex analysis in physics
NEXT STEPS
  • Study the graphical representation of wavefunctions in quantum mechanics
  • Explore the concept of scattering amplitudes in detail
  • Learn about the mathematical derivation of bound and non-bound state wavefunctions
  • Investigate the implications of poles in scattering theory
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Students of quantum mechanics, physicists specializing in wavefunction analysis, and researchers focusing on scattering theory will benefit from this discussion.

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Bound vs "not"bound states

Homework Statement


Hi, I do not understand how two bound state wavefunctions differ from not bound state
wavefunctions.
To be more precise I m thinking about the graphical representation.

ons[/b2. Relevant equati

The Attempt at a Solution


I speculate that bound states can overlap or get close to each other.
Perhaps the problem is in meaning of "bound" in this particuular case?
Could someone help me to understand this better?
 
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bound state wave functions are given by something like e(-kr)/r in comparison to non bound states for which WAVE FUNCTION at large distances are like Sle(ikr)/r+e(-ikr)/r where that Sl corresponds to scattering amplitude.You can see easily that bound state is just the pole for a replacement of K-->iK in scattering one because there is no incoming wave there.
 

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