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The wave function of an initially very localized free particle. In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters ψ and Ψ (lower-case and capital psi, respectively).
Superpositions of energy eigenstates change their properties according to the relative phases between the energy levels. The energy eigenstates form a basis: any wave function may be written as a sum over the discrete energy states or an integral over continuous energy states, or more generally as an integral over a measure.
In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential can be expressed as plane waves modulated by periodic functions. The theorem is named after the Swiss physicist Felix Bloch, who discovered the theorem in 1929. [1] Mathematically, they are written [2] Bloch function.
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.
In the framework of the de Broglie–Bohm theory, the quantum potential is a term within the Schrödinger equation which acts to guide the movement of quantum particles. . The quantum potential approach introduced by Bohm [1] [2] provides a physically less fundamental exposition of the idea presented by Louis de Broglie: de Broglie had postulated in 1925 that the relativistic wave function ...
Animation of the additive synthesis of a triangle wave with an increasing number of harmonics. See Fourier Analysis for a mathematical description.. It is possible to approximate a triangle wave with additive synthesis by summing odd harmonics of the fundamental while multiplying every other odd harmonic by −1 (or, equivalently, changing its phase by π) and multiplying the amplitude of the ...
Rectangular potential barrier. In quantum mechanics, the rectangular (or, at times, square) potential barrier is a standard one-dimensional problem that demonstrates the phenomena of wave-mechanical tunneling (also called "quantum tunneling") and wave-mechanical reflection. The problem consists of solving the one-dimensional time-independent ...
The most common description of the electromagnetic field uses two three-dimensional vector fields called the electric field and the magnetic field. These vector fields each have a value defined at every point of space and time and are thus often regarded as functions of the space and time coordinates. As such, they are often written as E(x, y ...