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Dirac Constant and The Golden Section
In physics, action is an attribute of the physical system dynamics. It has units of energy x time ( joule – seconds ). Planck`s constant is the quantum of action.
So we have this physical constant
Niels Bohr applies quantum theory to the Rutherford`s atomic structure by assuming that electrons travel in stationary orbits by their angular momentum. According to the Bohr the angular momentum in hydrogen atom is
Dirac`s constant used in quantum mechanics, equal to the Planck`s constant divided by . Also called crossed - h, h bar. Named after Paul Adrien Maurice Dirac ( 1902 – 1984 ) , English physicist. Planck`s constant, as the action, equals:
This result of Bohr`s hydrogen atom theory ( special case ) , become the de Broglie relation ( general case ). For the hydrogen atom the de Broglie relations are :
In an electromagnetic fields the wave - like behavior of small – momentum particles is analogous to that of light. On the other hand, in a gravitational fields the particles – like behavior of small – wave`s energy is analogous to that of electron.
Also we have Planck`s constant definition as:
The relation between fine structure constant and the golden section is:
The connection between Dirac`s constant and the Golden section is
On the other hand
This is the connection between Dirac`s constant and the value of the Golden Section
Where
