Sunday, November 19, 2017

Reduced Mass - Is the Discussion Over?

Time-dependent Schrödinger equation
(single nonrelativistic particle)
$$\mathbf{\hat{H}\Psi}= \mathbf{E\Psi}$$
$$i\hbar{\partial\over\partial t}\Psi(r,t)={\left[{-\hbar^2\over2{\color{red}\mu}}\nabla^2+V(r,t)\right]}\Psi(r,t)$$

$\mu=$ reduced mass <~~ this is the problem
$m^*=m_{eff}$ effective mass <~~ this is the problem
$\mu=m_{eff}$ BIG ASSUMPTION <~~ this is the problem

Experimentalists use this form of the Schrödinger equation to develop fields such as quantum electrodynamics (QED), solid-state electronics, and others.  They proceed and skip over the fact that the fundamental masses and constants are not defined.  While this will work somewhat for experiments, the theory is flawed.  It is leaving out important aspects relative to fundamental physics investigations.  Likely this has been well known for a long time but suppressed by savages masquerading as civilized humans.

So, this is the main problem with proceeding with using the reduced mass term in the Schrödinger equation.  When one proceeds using this equation and substituting the reduced mass term with an effective mass, $m_{eff}$, and proceed to develop a theory and test and measure and work with effective mass LIKE it IS the mass of the object under investigation, this is missing the behavior of the whole.  While experimental results can be obtained this way, it is missing a significant point.

This discussion of reduced mass has gone on so long that it has faded from discussion.  It requires careful considerations of mathematical and scientific integrity to even proceed.

The kind of thinking required is the same kind required to assemble a bicycle from Japan, parts from a box, on Christmas Eve, it requires much peace of mind. 

The Surfer, OM-IV

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