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When I learned the Uncertainty Principle, I noticed its similarity with the characteristics of the Fourier transform, but couldn't understand why. This paper sa

• tines 2y ago
  So the Fourier transform on wave functions is like integrating a normal function, like the velocity function, in Newtonian mechanics?
  • tomyedwab 2y ago
    That sounds more complicated than what is actually happening here. The way wave functions evolve over time, their velocity of movement is proportional to the frequency of oscillation. That is why measuring the frequency component of the wave function gives you the momentum function. You have to keep in mind that the wave function represents the many places the particle can be with some probability, as well as the many frequencies it could have, so what uncertainty means in this case is that if you constrain the function to a small area in space (with zero probability outside it) you necessarily end up with a momentum function that spreads across many different velocities.
  • jinwoo68 2y ago
    The similarity I noticed was the fact that in the Fourier transform, when the time domain graph is focused in a small time range, its frequency domain graph is spread out in a wide frequency range, and vice versa, like the position and the momentum in the uncertainty principle. That makes sense if the wave function of position is the Fourier transform of the wave function of momentum.