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  2. Square wave - Wikipedia

    en.wikipedia.org/wiki/Square_wave

    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.

  3. Helmholtz equation - Wikipedia

    en.wikipedia.org/wiki/Helmholtz_equation

    The Helmholtz equation has a variety of applications in physics and other sciences, including the wave equation, the diffusion equation, and the Schrödinger equation for a free particle. In optics, the Helmholtz equation is the wave equation for the electric field. [1] The equation is named after Hermann von Helmholtz, who studied it in 1860. [2]

  4. Schrödinger equation - Wikipedia

    en.wikipedia.org/wiki/Schrödinger_equation

    The resulting partial differential equation is solved for the wave function, which contains information about the system. In practice, the square of the absolute value of the wave function at each point is taken to define a probability density function.

  5. Wave function - Wikipedia

    en.wikipedia.org/wiki/Wave_function

    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.

  6. Quantum harmonic oscillator - Wikipedia

    en.wikipedia.org/wiki/Quantum_harmonic_oscillator

    Furthermore, the square of the amplitude (determining the probability density) is inversely proportional to p(x), reflecting the length of time the classical particle spends near x. The system behavior in a small neighborhood of the turning point does not have a simple classical explanation, but can be modeled using an Airy function .

  7. Envelope (waves) - Wikipedia

    en.wikipedia.org/wiki/Envelope_(waves)

    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]

  8. Coulomb wave function - Wikipedia

    en.wikipedia.org/wiki/Coulomb_wave_function

    The Coulomb wave equation for a single charged particle of mass is the Schrödinger equation with Coulomb potential [1] (+) = (),where = is the product of the charges of the particle and of the field source (in units of the elementary charge, = for the hydrogen atom), is the fine-structure constant, and / is the energy of the particle.

  9. Optical transfer function - Wikipedia

    en.wikipedia.org/wiki/Optical_transfer_function

    Either transfer function specifies the response to a periodic sine-wave pattern passing through the lens system, as a function of its spatial frequency or period, and its orientation. Formally, the OTF is defined as the Fourier transform of the point spread function (PSF, that is, the impulse response of the optics, the image of a point source).