Ansatz

From McGill University Physics Department Technical Services Wiki

Ansatz is a German language term often used by physicists and mathematicians. An ansatz is the establishment of the starting equation(s) describing a mathematical or physical problem. It can take into consideration boundary conditions. After an ansatz has been established, the equations are solved for the general function of interest. Typically, a word problem starts by writing down the ansatz with subsequent refinenement leading to the solution of the problem. The German word Ansatz means something like "basis" or "starting point."

For example, given a set of experimental data that looks to be clustered about a line, a linear ansatz could be made to find the parameters of the line by a least squares curve fit. Variational approximation methods use ansätze and then fit the parameters.

Another example of ansatz is to suppose the solutions of a homogeneous linear differential equation and difference equation to have, respectively, exponential and power form. More generally one can guess a particular solution of a system of equations and test such an ansatz by direct substitution of the solution in the system of equations.

See Also

• Ersatz (http://en.wikipedia.org/wiki/Ersatz)