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  2. Wave packet - Wikipedia

    en.wikipedia.org/wiki/Wave_packet

    If (,) (and therefore ()) is a Gaussian function, the wave packet is called a Gaussian wave packet. [12] For example, the solution to the one-dimensional free Schrödinger equation (with 2Δx, m, and ħ set equal to one) satisfying the initial condition (,) = / ⁡ (+), representing a wave packet localized in space at the origin as a Gaussian ...

  3. Uncertainty principle - Wikipedia

    en.wikipedia.org/wiki/Uncertainty_principle

    This wave packet becomes increasingly localized with the addition of many waves. The Fourier transform is a mathematical operation that separates a wave packet into its individual plane waves. The waves shown here are real for illustrative purposes only; in quantum mechanics the wave function is generally complex .

  4. Group velocity - Wikipedia

    en.wikipedia.org/wiki/Group_velocity

    The expanding ring of waves is the wave group or wave packet, within which one can discern individual waves that travel faster than the group as a whole. The amplitudes of the individual waves grow as they emerge from the trailing edge of the group and diminish as they approach the leading edge of the group.

  5. Wavelet packet decomposition - Wikipedia

    en.wikipedia.org/wiki/Wavelet_packet_decomposition

    Wavelet Packet Decomposition is a powerful signal processing technique that offers a multi-resolution analysis of the timber's moisture content. This approach allows for a detailed examination of the signal at different frequency bands, providing a more comprehensive understanding of the moisture distribution within the material.

  6. Quantum tunnelling - Wikipedia

    en.wikipedia.org/wiki/Quantum_tunnelling

    A portion of the wave packet passes through the barrier. The wave function of a physical system of particles specifies everything that can be known about the system. [8] Therefore, problems in quantum mechanics analyze the system's wave function. Using mathematical formulations, such as the Schrödinger equation, the time evolution of a known ...

  7. Slowly varying envelope approximation - Wikipedia

    en.wikipedia.org/wiki/Slowly_varying_envelope...

    Consequently, the wave equation is approximated in the SVEA as: + = . It is convenient to choose k 0 and ω 0 such that they satisfy the dispersion relation: = . This gives the following approximation to the wave equation, as a result of the slowly varying envelope approximation:

  8. Davey–Stewartson equation - Wikipedia

    en.wikipedia.org/wiki/Davey–Stewartson_equation

    In fluid dynamics, the Davey–Stewartson equation (DSE) was introduced in a paper by A. Davey and Keith Stewartson to describe the evolution of a three-dimensional wave-packet on water of finite depth.

  9. List of equations in wave theory - Wikipedia

    en.wikipedia.org/wiki/List_of_equations_in_wave...

    The phase velocity is the rate at which the phase of the wave propagates in space. The group velocity is the rate at which the wave envelope, i.e. the changes in amplitude, propagates. The wave envelope is the profile of the wave amplitudes; all transverse displacements are bound by the envelope profile.

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