For example, may be one or more linear combinations of .

So a solution on the edge can be written as a linear combination of plane waves.

The general solution is any linear combination of these two.

To do this, one must add all powers of "X" and their linear combinations as well.

The final wave function is a linear combination of these two functions.

The coefficients or weights of the linear combination can be learned as well.

One can work with more familiar variables as linear combinations of these.

Now and is thus, in general a linear combination of 1,.

Therefore, the only possible way to get a linear combination is with these coefficients.

Whether the other linear combinations are useful is a different matter, but one cannot just throw away possible solutions "without cause".