Re: Imaginary reality

[Jack Uretsky <jlu@HEP.ANL.GOV>]

        Well, it depends on what you want to do with your wave equation.
If you want to consider transmission-reflection problems through a
boundary, it's usually easier to work with exponential solutions (and
complex reflection and transmission) coefficients.  At the end, you
take the real (or imaginary) part of your solutions.  In the meantime
you have saved yourself some work adding trig and subtracting trig
functions at the boundary.
        Your students will eventually repeat the identical calculations
when they solve square-well problems in QM.
                                Regards,
                                        Jack


Adam was by constitution and proclivity a scientist; I was the same, and
we loved to call ourselves by that great name...Our first memorable
scientific discovery was the law that water and like fluids run downhill,
not up.
                          Mark Twain, <Extract from Eve's Autobiography>

On Sat, 22 Apr 2000, Ben Crowell wrote:

> In classical E&M, it seems to me that the only point of using
> complex numbers is to simplify notation, e.g. to be able to write
> a Fourier analysis with only one function, the exponential, rather
> than 2, sines and cosines.
>
> On the other hand, a quantum mechanical electron's
> wavefunction happens to obey the same rules as complex
> arithmetic. The theory is actually incomplete without
> complex numbers, in the same way that you can't make
> a complete theory of the quadratic equation without them.
>
> Since the original question was about pedagogy, this seems
>  to me a good argument for waiting until QM to introduce
> complex waves.
>
>     Ben Crowell
>     Fullerton College