Proving Acceptable Wave Functions in Quantum Mechanics

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SUMMARY

The discussion focuses on proving the acceptability of wave functions in quantum mechanics, specifically within the context of an infinite square well. Key criteria for an acceptable wave function include being zero outside the defined boundaries and being normalizable, as expressed by the integral condition ∫ |Ψ(x,t)|² dx = 1. Additionally, it is established that as long as the wave function is a member of Hilbert Space, it qualifies as acceptable, emphasizing the importance of continuity and normalizability in this context.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly wave functions.
  • Familiarity with Hilbert Space concepts in quantum theory.
  • Knowledge of normalization conditions for wave functions.
  • Basic grasp of the infinite square well model in quantum mechanics.
NEXT STEPS
  • Study the properties of Hilbert Space in quantum mechanics.
  • Learn about normalization techniques for wave functions.
  • Explore examples of non-acceptable wave functions and their characteristics.
  • Investigate the implications of boundary conditions in quantum systems.
USEFUL FOR

Students of quantum mechanics, physicists focusing on wave functions, and educators teaching quantum theory concepts.

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Homework Statement



[PLAIN]http://img716.imageshack.us/img716/8330/werhc.png

Homework Equations





The Attempt at a Solution



My question is what do I need to prove to show that the wave function is acceptable. So far all I can think of is showing that the wave function is 0 outside the boundaries (infinite square well) and that the equation can be normalized. [tex]\int |\Psi(x,t)|^2dx=1[/tex]
Am I missing any postulates? Also, if someone could give me an example of how a wave function isn't spatial it would help a lot.
 
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As long as the wave function is a member of Hilbert Space, the wave function is acceptable. So in this case, continuous and normalizable is okay.
 

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