Confusion about Fourier transforms and conjugate variables…
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Confusion about Fourier transforms and conjugate variables
My quantum mechanics notes state that conjugate variables (like position and momentum) are Fourier duals of each other. I understand how this shows up in the mathematics, but I’m confused about the deeper meaning:
* Where does the notion of conjugate variables actually come from?
* Why are they related by a Fourier transform?
Related to this, I learned that a Hermitian operator generates a unitary operator via exponentiation. The Fourier transform is a unitary operator. Which Hermitian operator has an exponential giving the Fourier transform?
#science
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My quantum mechanics notes state that conjugate variables (like position and momentum) are Fourier duals of each other. I understand how this shows up in the mathematics, but I’m confused about the deeper meaning:
* Where does the notion of conjugate variables actually come from?
* Why are they related by a Fourier transform?
Related to this, I learned that a Hermitian operator generates a unitary operator via exponentiation. The Fourier transform is a unitary operator. Which Hermitian operator has an exponential giving the Fourier transform?
#science
source
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