What is the relationship between frequency and wave function?

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SUMMARY

The relationship between frequency and wave function is defined by the complex phase factor in quantum mechanics, represented as ##e^{i \omega t}##, where ##\omega = 2 \pi f##. The wave function describes the position of a particle with probability amplitude, and while it is not a wave, it can be conceptualized as a vibration field in the complex plane. This understanding clarifies the role of frequency in the context of wave functions.

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phyky
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wave function always refer to the position of particle with probability amplitude. since wave function is not a wave but field, frequency seems meaningless to it. can i imagine it is a vibration field with certain frequency f in complex plane or something?
 
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phyky said:
vibration field with certain frequency f in complex plane or something?

That's exactly what it is. A wave function generally has a complex phase factor of the form ##e^{i \omega t} = \cos (\omega t) + i \sin (\omega t)## where ##\omega = 2 \pi f##.
 

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