A PID controller continuously calculates an " error value " e ( t ) as the difference between a desired proportional, integral, and derivative terms . " PID " is an initialism for " Proportional-Integral-Derivative ", referring to the three terms operating on the error signal to produce a control signal.
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It integrates exp ( ? " F " ) over all values of " H ", over all the long wavelength fourier components of the spins . " F " is a Euclidean Lagrangian for the field " H ", the only difference between this and the quantum field theory of a scalar field is that all the derivative terms enter with a positive sign, and there is no overall factor of " i ".
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What you need to do then is to show that if \ psi ( x ) is an energy eigenfunction with energy eigenvalue E, then than implies that \ psi ( x ) ^ { * } is also an eigenfunction with eigenvalue E ( Hint : take the complex conjugate of the time independent Schrodinger equation and write that in terms of \ psi ( x ) ^ { * }, the main issue here is to correctly treat the second derivative term ) . talk ) 17 : 42, 24 March 2014 ( UTC)
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