Checking Note 433(4)

Yes agreed, it is rigorously correct to derive Eq. (9) from the classical eq. (7). I double checked the plane wave solution and found the same answer, just transmitted in Note 433(6) .It can be triple checked with Maxima.

Checking Note 433(4)

Two comments concerning the note:
1. Eq. (9) cannot be derived from (8) because for two operators A, B

<A> / <B> =! <A/B>.

However eq.(9) can be derived from (7) directly.

2. Plane wave solutions (for a function f) require an equation of type

d^2 f/dx^2 + omega^2 f = 0.

There must be two plus sign. The d’Alembere operator, however, contains a minus sign for the space part, leading to

d^2 f/dx^2 – omega^2 f = 0.

This equation has no oscillatory but exponentially growing and falling solutions. I guess that a minus sign has to be used in front of the mc/hbar factor. Perhaps this has been overlooked when deriving this equation from the ECE wave equation, i.e. the sign of the curvature R has been interchanged accidentally.

Horst

Am 10.03.2019 um 11:09 schrieb Myron Evans:


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