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Delta function & kronecker delta

  1. May 22, 2005 #1
    Can anyone tell me the difference between the Delta function and the Kronecker delta?

    It seems that both are 1 at a certain point and 0 otherwise...

    The delta function is a eigenfunction of x and the Kronecker delta is ...

    i'm kind of confused..
     
  2. jcsd
  3. May 22, 2005 #2

    mathman

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    Delta function: Integral of f(x) F(x-a), where F is the delta function,
    =f(a) when a is in the interval, and integral =0 if a is not in the interval.

    Kronecker delta G(n-k) (usually for integer argument, not real) G=1 for n=k, =0 for n not=k.
     
  4. May 22, 2005 #3

    quasar987

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    From what I understand, the kronecker delta is just an abreviation. For exemple, if we have a set of orthonormal vectors [itex]\hat{e}_{i}[/itex]

    Then the dot product of any two of these vectors can be expressed as

    [tex](\hat{e}_{n}|\hat{e}_{k}) = \left\{\begin{array}{rcl}1 \ \mbox{if} \ n=k\\ 0 \ \mbox{otherwise}\end{array}[/tex]

    So we write

    [tex](\hat{e}_{n}|\hat{e}_{k}) = \delta_{nk}[/tex]

    to compactly express this fact.
     
  5. May 22, 2005 #4
    delta function

    The delta function, delta(x), is infinite at x=0, zero everywhere else. It is what a normalized Gaussian "hump" looks like in the limit as its width goes to zero.

    In contrast, Kronecker delta is not really a function at all ... more like an element of a matrix (the identity matrix). So Kronecker[ij] = 1 (if i==j), or 0 (if i!=j).
     
  6. May 22, 2005 #5

    dextercioby

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    Delta-Dirac is a distribution,while Delta-Kronecker is an invariant totally symmetrical tensor of arbitrary rank.

    Daniel.
     
  7. May 23, 2005 #6

    aav

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    Also, both are used to express orthogonality, given a set of vectors, the arguments being the indices of the two vectors in question: the kronecker delta if that set is countable, the delta function if otherwise.
     
  8. May 23, 2005 #7
    in an easy language, they are inherently the same (they have the same/analoguous meaning) but the Kronecker delta is the DISCRETE variant of the delta dirac distribution/functional. So the indices are discrete where they are continuous (they vary continuously) in case of the delta dirac distribution.

    regards

    marlon
     
  9. May 23, 2005 #8

    dextercioby

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    In de Witt notation,where the D-dim delta-Dirac is supressed,one only finds the Kronecker one.However,the Dirac one is commonly understood.

    Daniel.
     
  10. May 16, 2009 #9
    Re: delta function & kronecker delta

    [tex]\delta[/tex]ij constitutes the identity matrix when:

    ([tex]\delta[/tex]ij)i,jn [that's NOT j to the n]
     
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