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Examples

It would be useful to do a course on FEM because that way, the idea of using "ansatz" seems to begin to become more "natural."

Get comfortable with the idea that the "ansatz" or the assumed form for the solution/potential form is purely arbitrary, even though no selfrespecting author of mechanics/analytical mathematics would ever highlight this particular part about the analytical theory.

Again, however, Stenger's paper demonstrates an ignorance of the relevant literature in the philosophy of physics, some of which is somewhat less enthusiastic about the HartleHawking ansatz ...

An ansatz to the ‘Talk Like a Physicist’ problem: Throw in random German words, like ‘brehmsstahlung’ and ‘zitterbewegung’.

And what about the “homogeneous distribution” ansatz of FRW?

PS – according to Mathworld, “An ansatz is an assumed form for a mathematical statement that is not based on any underlying theory or principle.”

The logarithm rule is an empirical rule of thumb ansatz? which describes the net result in ranges of interest, considering various isotopes, far bands, hot bands etc. , with the combination of changing linear and saturation effects being approximated by a logarithm.

It is of course possible for a solution to concentrate its mass and energy in a different configuration than a bump function; but experience has shown that the most nonlinear behaviour tends to occur when such a concentration occurs, and so this ansatz is expected to capture the "worstcase" behaviour of the solution.

(One can also refine the above ansatz in a number of ways, for instance by also introducing a frequency modulation, which is particularly important in models such as the masscritical NLS which admit a frequency modulation symmetry, but for simplicity we will not consider this more complicated situation here.)

These considerations illustrate how the commonly used semigroup ansatz for time evolution of the unstable systems arises.
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