**Appendix
D**

** **

In the
spherical polar coordinate axes (_{}), the gradient is:

_{}

The spherical wave equation is:

_{}

Where ‘*v’* is the speed of the wave which propagate
through radial direction, for the special case in which it has angular symmetry
(not dependent on the _{}), then we will have the following wave equation:

_{}

Thus:

_{}

Thus, we have the following
general solution:

_{}

Thus:

_{}

In which

_{}

Where k is the wave number.

_{}

Where w is the angular frequency.

What
is the electron spin?
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