A FOURIER THEOREM AND ITS APPLICATION TO THE MEASUREMENT OF ELECTROMAGNETIC FIELDS AND QUANTUM MECHANICAL STATES

Abstract : A mathematical theorem is presented by which one can determine in an essentially unique way a complex function of a real argument from its absolute value and the absolute values of the Fourier transform of the truncated function for all possible truncations. The absolute values of the function and of the Fourier transforms have a physical significance in electromagnetic and quantum theory. The theorem presented enables one to assign electric fields to energy densities and quantum mechanical states to sets of probability densities. The measurements required for use in quantum mechanics can be expressed as the mean values of certain operators constructed from the position and momentum operators.