What is the relationship between frequency and wave function?

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The wave function is associated with the position of a particle and represents probability amplitude rather than a traditional wave. While it is not a wave itself, it can be conceptualized as a vibration field with a frequency in the complex plane. The relationship between frequency and wave function is expressed through a complex phase factor, which incorporates frequency into its formulation. This phase factor is mathematically represented as e^(iωt), where ω is related to frequency f. Understanding this relationship enhances the comprehension of wave functions in quantum mechanics.
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##.
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

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