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Typically, the potential is modelled as a Heaviside step function.
In mathematics, sometimes used to denote the Heaviside step function.
He invented the Heaviside step function and employed it to model the current in an electric circuit.
For instance, it is the distributional derivative of the Heaviside step function.
The Heaviside step function can be represented as .
The Heaviside step function in its discrete form is an example of a bang-bang control signal.
Often an integral representation of the Heaviside step function is useful:
The function looks like , where is the Heaviside step function.
A particular indicator function, which is very well known, is the Heaviside step function.
The Fourier transform of the Heaviside step function is a distribution.
The convolution of the Heaviside step function with itself:
The value of H(0) will depend upon the particular convention chosen for the Heaviside step function.
As a transfer function, it employed a threshold, equivalent to using the Heaviside step function.
The Heaviside step function multiplied by a straight line with unity gradient:
Alternatively, this can be defined using the Heaviside step function, H(x).
The sign function and Heaviside step function are also easily expressed in this notation:
See Heaviside step function - Analytic approximations.
The Heaviside step function, often denoted by u(t):
The error and complementary error functions occur, for example, in solutions of the heat equation when boundary conditions are given by the Heaviside step function.
The step potential is simply the product of V, the height of the barrier, and the Heaviside step function:
In higher dimensions, the indicator function of a domain still makes sense, and thus makes a natural generalization of the Heaviside step function.
The function 1 equals 1 on the positive halfline and zero otherwise, and is also known as the Heaviside step function.
We can also define an alternative form of the Heaviside step function as a function of a discrete variable n:
It can also be defined with respect to the Heaviside step function u(t) or the rectangular function (t):
The Heaviside step function is the indicator function of the one-dimensional positive half-line, i.e. the domain [0, ).
