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The square wave in mathematics has many definitions, which are equivalent except at the discontinuities: It can be defined as simply the sign function of a sinusoid: = () = () = () = (), which will be 1 when the sinusoid is positive, −1 when the sinusoid is negative, and 0 at the discontinuities.
In this case, the wave functions are square integrable. One can initially take the function space as the space of square integrable functions, usually denoted L 2. The displayed functions are solutions to the Schrödinger equation. Obviously, not every function in L 2 satisfies the Schrödinger equation for the hydrogen atom.
A modulated wave resulting from adding two sine waves of identical amplitude and nearly identical wavelength and frequency. A common situation resulting in an envelope function in both space x and time t is the superposition of two waves of almost the same wavelength and frequency: [2]
The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves). It arises in fields like acoustics, electromagnetism, and fluid dynamics.
Functional approximation of square wave using 5 harmonics Functional approximation of square wave using 25 harmonics Functional approximation of square wave using 125 harmonics. The Gibbs phenomenon is a behavior of the Fourier series of a function with a jump discontinuity and is described as the following:
The relative contrast is given by the absolute value of the optical transfer function, a function commonly referred to as the modulation transfer function (MTF). Its values indicate how much of the object's contrast is captured in the image as a function of spatial frequency.
The quantum jump method is an approach which is much like the master-equation treatment except that it operates on the wave function rather than using a density matrix approach. The main component of this method is evolving the system's wave function in time with a pseudo-Hamiltonian; where at each time step, a quantum jump (discontinuous ...
Consequently, the wave function also became a four-component function, governed by the Dirac equation that, in free space, read (+ (= )) =. This has again the form of the Schrödinger equation, with the time derivative of the wave function being given by a Hamiltonian operator acting upon the wave function.