compound ket fn: Gaussian

Gaussian:
    description:
        Gaussian[sigma] ket
        Gaussian[sigma, dx] ket
        implements a Gaussian superposition centred on ket, with sigma the standard deviation
        if dx is not specified, it defaults to 1, where dx is step size

    the algorithm:
        exp( - ED(x, y) / (2 * sigma ^ 2))
        where ED(x, y) is the Euclidean distance between x and y

    examples:
        Gaussian[0.7] |40>
            0.016880|36> + 0.046830|37> + 0.129923|38> + 0.360448|39> + |40> + 0.360448|41> + 0.129923|42> + 0.046830|43> + 0.016880|44>

        -- bar-chart of 1D version:
        bar-chart[50] Gaussian[0.7] |age: 35>
            ----------
            age: 31 : |
            age: 32 : ||
            age: 33 : ||||||
            age: 34 : ||||||||||||||||||
            age: 35 : ||||||||||||||||||||||||||||||||||||||||||||||||||
            age: 36 : ||||||||||||||||||
            age: 37 : ||||||
            age: 38 : ||
            age: 39 : |
            ----------

        -- 2D version:
        Gaussian[0.5] |10: 10>
            0.003493|8: 8> + 0.011423|8: 9> + 0.018316|8: 10> + 0.011423|8: 11> + 0.003493|8: 12> + 0.011423|9: 8> + 0.059106|9: 9> + 0.135335|9: 10> + 0.059106|9: 11> + 0.011423|9: 12> + 0.018316|10: 8> + 0.135335|10: 9> + |10: 10> + 0.135335|10: 11> + 0.018316|10: 12> + 0.011423|11: 8> + 0.059106|11: 9> + 0.135335|11: 10> + 0.059106|11: 11> + 0.011423|11: 12> + 0.003493|12: 8> + 0.011423|12: 9> + 0.018316|12: 10> + 0.011423|12: 11> + 0.003493|12: 12>

    see also: