Bill Larson asked:
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I understand how to rewrite grad V =3D dp/dt as three equations,
but can you rewrite the Schroedinger equation as 2 equations =
for me? Is it somehow using Euler's equation? Since it's
psi* psi that has physical reality, I'd suppose the real and =
imaginary do not independently have physical reality. Right?
Bill Larson
Geneva
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Bill,
Define the real and imaginary parts of PSI:
PSI(r,t) = U(r,t) + i * V(r,t), where U and V are real.
Put this into the Shroedinger equation and equate reals and
imaginaries in two separate equations.
PS.
You get a different insight if you define the magnitude
and phase of the complex Psi:
PSI(r,t) = M(r,t)*exp(i*PHI(r,t)) All three representations
are of course equivalent.
PPS
I'm not sure what your question about physical reality means.
Does the acceleration of a car have physical reality?
Whether you choose to make them explicit or not, the real and
imaginary parts of PSI are (or are not) just as "real" as is
(or is not) PSI!