Some system can be normalized, some can not

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SUMMARY

This discussion centers on the normalization of wavefunctions in quantum mechanics (QM), specifically addressing scenarios where normalization is possible and where it is not. It is established that wavefunctions for particles in free space cannot be normalized due to their unbound nature. The conversation highlights that while idealized models like plane waves present challenges in normalization, more realistic models such as wave packets can be normalized. The dialogue emphasizes the importance of context in understanding these normalization issues.

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Black Integra
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I'm new and have been studying QM myself for a while. I have a little question about normalization.
Some system can be normalized, some can not (such as potential step).
What does it mean? And how can we solve these problems?
 
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What it means depends on the system.

For instance you cannot normalize the wavefunction for a particle in free space because the particle is not bound.

We don't normally need to "solve" them because we normally have more information than that. Like our particle "in free space" is probably traveling from some interaction to another one ... so it is not actually "free". These puzzles are only used for beginning students to get you used to the math.
 


Black Integra said:
I'm new and have been studying QM myself for a while. I have a little question about normalization.
Some system can be normalized, some can not (such as potential step).
What does it mean? And how can we solve these problems?
I'm very new to QM (taking my first introductory course) but do you mean the case of a plane wave incident on a potential step? If so, it might be because plane waves are an idealization and for a closer to reality model, we take a wavefunction Psi equal to a wave packet rather than a plane wave. I think in that case Psi can be normalized. I may have misunderstood your question though. Feel free to give more details.
 

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