• Thumbnail for Dirac delta function
    mathematical analysis, the Dirac delta function (or δ distribution), also known as the unit impulse, is a generalized function on the real numbers, whose...
    94 KB (14,099 words) - 16:33, 15 December 2024
  • function is often confused for both the Kronecker delta function and the unit sample function. The Dirac delta is defined as: { ∫ − ε + ε δ ( t ) d t = 1 ∀...
    22 KB (4,056 words) - 21:53, 29 December 2023
  • Thumbnail for Dirac comb
    }\delta (t-kT)} for some given period T {\displaystyle T} . Here t is a real variable and the sum extends over all integers k. The Dirac delta function...
    20 KB (3,462 words) - 09:42, 2 October 2024
  • Thumbnail for Dirac measure
    of formalizing the idea of the Dirac delta function, an important tool in physics and other technical fields. A Dirac measure is a measure δx on a set...
    6 KB (640 words) - 04:31, 19 December 2022
  • quantum mechanics the delta potential is a potential well mathematically described by the Dirac delta function - a generalized function. Qualitatively, it...
    16 KB (2,714 words) - 10:00, 18 August 2024
  • Thumbnail for Heaviside step function
    integral of the Dirac delta function. This is sometimes written as H ( x ) := ∫ − ∞ x δ ( s ) d s {\displaystyle H(x):=\int _{-\infty }^{x}\delta (s)\,ds} although...
    14 KB (2,100 words) - 00:39, 12 November 2024
  • Thumbnail for Impulse response
    function contains all frequencies (see the Fourier transform of the Dirac delta function, showing infinite frequency bandwidth that the Dirac delta function...
    10 KB (1,223 words) - 12:58, 25 March 2024
  • Thumbnail for Rectangular function
    {\displaystyle \delta (t)} is δ ( f ) = 1 , {\displaystyle \delta (f)=1,} means that the frequency spectrum of the Dirac delta function is infinitely broad...
    11 KB (1,668 words) - 19:47, 9 December 2024
  • Thumbnail for Green's function
    Green's function G {\displaystyle G} is the solution of the equation L G = δ {\displaystyle LG=\delta } , where δ {\displaystyle \delta } is Dirac's delta function;...
    38 KB (5,166 words) - 20:01, 12 December 2024
  • A Dirac delta function or simply delta function is a generalized function on the real number line denoted by δ that is zero everywhere except at zero...
    813 bytes (150 words) - 03:41, 17 December 2022
  • Thumbnail for Sign function
    in distribution theory, the derivative of the signum function is two times the Dirac delta function. This can be demonstrated using the identity sgn ⁡ x...
    16 KB (2,791 words) - 01:56, 12 December 2024
  • The Kronecker delta in mathematics The degree of a vertex (graph theory) The Dirac delta function in mathematics The transition function in automata Deflection...
    11 KB (1,327 words) - 18:05, 17 December 2024
  • Laplacian of the indicator (category Generalized functions)
    of the Dirac delta function to higher dimensions, and is non-zero only on the surface of D. It can be viewed as the surface delta prime function. It is...
    30 KB (4,258 words) - 06:02, 14 June 2024
  • Thumbnail for Paul Dirac
    career, Dirac made numerous important contributions to mathematical subjects, including the Dirac delta function, Dirac algebra and the Dirac operator...
    90 KB (9,883 words) - 23:41, 19 December 2024
  • functions. Symmetric function: value is independent of the order of its arguments Generalized function: a wide generalization of Dirac delta function...
    13 KB (1,407 words) - 06:43, 10 October 2024
  • Thumbnail for Fourier transform
    relatively simple applications use the Dirac delta function, which can be treated formally as if it were a function, but the justification requires a mathematically...
    175 KB (20,877 words) - 09:30, 14 December 2024
  • Thumbnail for Wave function
    potentials that are not functions but are distributions, such as the Dirac delta function. It is easy to visualize a sequence of functions meeting the requirement...
    99 KB (13,587 words) - 16:07, 13 December 2024
  • function of two discrete variable m and n. Similar to the case of Dirac delta function for continuous variables, it is defined to be 1 if m = n and 0 otherwise...
    25 KB (3,514 words) - 23:59, 1 February 2024
  • three-dimensional space, and δ {\displaystyle \delta } is the Dirac delta function. The algebraic expression of the Green's function for the three-variable Laplace operator...
    11 KB (1,910 words) - 01:17, 15 August 2024
  • arguments. The integral of the Dirac delta function. Sawtooth wave Square wave Triangle wave Rectangular function Floor function: Largest integer less than...
    10 KB (1,065 words) - 20:52, 29 October 2024
  • 1920s and 1930s further basic steps were taken. The Dirac delta function was boldly defined by Paul Dirac (an aspect of his scientific formalism); this was...
    18 KB (2,202 words) - 17:25, 24 November 2024
  • Thumbnail for Probability density function
    the probability density function of X {\displaystyle X} and δ ( ⋅ ) {\displaystyle \delta (\cdot )} be the Dirac delta function. It is possible to use...
    30 KB (4,935 words) - 08:01, 15 December 2024
  • introduction of several component wave functions in Pauli's phenomenological theory of spin. The wave functions in the Dirac theory are vectors of four complex...
    79 KB (13,053 words) - 18:11, 7 December 2024
  • distribution of a function Difference operator (Δ) Dirac delta functionfunction) Kronecker delta ( δ i j {\displaystyle \delta _{ij}} ) Laplace operator...
    9 KB (1,139 words) - 06:02, 26 November 2024
  • Thumbnail for Infinitesimal
    continuity in his Cours d'Analyse, and in defining an early form of a Dirac delta function. As Cantor and Dedekind were developing more abstract versions of...
    37 KB (5,092 words) - 03:39, 3 December 2024
  • Thumbnail for Point (geometry)
    as points with non-zero charge). The Dirac delta function, or δ function, is (informally) a generalized function on the real number line that is zero...
    14 KB (1,608 words) - 05:39, 1 October 2024
  • Thumbnail for Beta distribution
    distribution becomes a one-point degenerate distribution with a Dirac delta function spike at the right end, x = 1, with probability 1, and zero probability...
    244 KB (40,545 words) - 06:26, 16 December 2024
  • the step response to a step input, or the impulse response to a Dirac delta function input. In the frequency domain (for example, looking at the Fourier...
    20 KB (2,993 words) - 20:24, 18 September 2024
  • Thumbnail for Indicator function
    Heaviside step function is equal to the Dirac delta function, i.e. d H ( x ) d x = δ ( x ) {\displaystyle {\frac {dH(x)}{dx}}=\delta (x)} and similarly...
    17 KB (2,417 words) - 19:54, 28 November 2023
  • {\displaystyle x} is the Dirac delta (function) distribution centered at the position x {\displaystyle x} , often denoted by δ x {\displaystyle \delta _{x}} . In quantum...
    16 KB (2,617 words) - 10:26, 17 October 2024