It is a characteristic of Quantum Mechanics that conjugate variables are Fourier transform pairs of variables.
As x and k form a Fourier transform pair in quantum mechanics, the Nyquist-Shannon Sampling theorem must also apply to this pair of conjugate variables.
Equations (32) and (35) are recognized as measurement relationships for quantummechanical conjugate variables.
The reason is that one expression involves the widths of conjugate variables as determined by (1) to (3), while the other involves sampling a variable and truncating its conjugate, or vice versa as determined by (32) and (35).
Quantum mechanical conjugate variables are Fourier Transform pairs of variables.
We have shown from Fourier Transform theory that the Nyquist-Shannon Sampling Theorem affects the nature of measurements of quantum mechanical conjugate variables.
We have noted that both the Sampling Theorem and the Uncertainty Theorem are required to fully describe quantum mechanical conjugate variables.
Sampling a variable x at a rate [delta]x will result in the measurement of its conjugate variable [?