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May I pursue the Q about complex wave amplitudes a little
differently (but it's still
pedagogy). Accepting that complex expressions are useful in
handling phase in
electrical circuits, let's assume that students would know
about 2-vector space,
one way or another, early on. My question, directed toward
teachers of QM, is ...
when (chronologically) are students expected to understand
that approaches to
the TISE must be via complex wave amplitude expressions
(Aexp[i(kx-wt)])? And
how (where) is this expectation introduced to the student's
sense of mind's-eye reality? In fact, is this possible in the first place? For
example would one say..
"Students, you will have to learn a wave amplitude _expression_
quite different than
the one that models the surface of a ripple tank. No longer
will y=Acos(kx) suffice; rather a complex wave (no picture)..etc..Later you'll
see the practical reality"
sincerely Tim
Wagner
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