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Hartley oscillator using a common-drain n-channel JFET instead of a tube.. The Hartley oscillator is distinguished by a tank circuit consisting of two series-connected coils (or, often, a tapped coil) in parallel with a capacitor, with an amplifier between the relatively high impedance across the entire LC tank and the relatively low voltage/high current point between the coils.
The quantum harmonic oscillator; The quantum harmonic oscillator with an applied uniform field [1] The Inverse square root potential [2] The periodic potential The particle in a lattice; The particle in a lattice of finite length [3] The Pöschl–Teller potential; The quantum pendulum; The three-dimensional potentials The rotating system The ...
The Hartley function only depends on the number of elements in a set, and hence can be viewed as a function on natural numbers. Rényi showed that the Hartley function in base 2 is the only function mapping natural numbers to real numbers that satisfies
Ralph Vinton Lyon Hartley (November 30, 1888 – May 1, 1970) was an American electronics researcher. He invented the Hartley oscillator and the Hartley transform, and contributed to the foundations of information theory. His legacy includes the naming of the hartley, a unit of information equal to one decimal digit, after him.
A common application of this is in the Hartley oscillator. Inductors with taps also permit the transformation of the amplitude of alternating current (AC) voltages for the purpose of power conversion, in which case, they are referred to as autotransformers , since there is only one winding.
In particular, the DHT analogue of the Cooley–Tukey algorithm is commonly known as the fast Hartley transform (FHT) algorithm, and was first described by Bracewell in 1984. [5] This FHT algorithm, at least when applied to power-of-two sizes N , is the subject of the United States patent number 4,646,256, issued in 1987 to Stanford University .
As before, the Rabi problem is solved by assuming that the electric field E is oscillatory with constant magnitude E 0: = (+). In this case, the solution can be found by applying two successive rotations to the matrix equation above, of the form
The coefficients of the super-harmonic terms are solved directly, and the coefficients of the harmonic term are determined by expanding down to order-(n+1), and eliminating its secular term. See chapter 10 of [ 5 ] for a derivation up to order 3, and [ 8 ] for a computer derivation up to order 164.