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I Generating a Hilbert space representation of a wavefunction

  1. Nov 8, 2017 #41


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    Vanhees, it's Molecular Quantum Mechanics

    Mark, I read your suggestion with care now, and I noticed I already did what you wrote, however, I called it the hat function a "testing function", as derived from one of Bills links. The testing function is 1, and the integral is for 1 * Psi over the interval 0 to 2pi, which makes it a tempered distribution, allowed for Fourier Transform.

    Whether it makes any physical sense is not the scope of this paper, however, I have done a Hilbert transform of it, to see its behaviour as a signal in a physical world.

    Bill, I will look into the Dirac function alternative.

    Thanks all
  2. Nov 8, 2017 #42


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    I didnt say a vector is orthogonal, I said the wavefunction is non-ortogonal to its complex conjugate, which is the reason for the overlap integral being a non-zero value. However, the very function is square integrable over a finite region, and it is normalizable. Untitled.jpg
  3. Nov 8, 2017 #43


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    Please read the passage you quoted again carefully word by word! Nowhere it's said a wave function is orthogonal or non-orthogonal to its complex conjugate. This wouldn't make any sense! It doesn't matter whether you work in molecular quantum mechanics or any other application, the math of QM is unique.
  4. Nov 8, 2017 #44


    Staff: Mentor

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