High School Is Energy Truly Quantized in De Broglie's Equation?

[_PJ_]

Given De Broglie's equations of a quantised wave:

E = 2.Pi.hbar.c

Where:
E = Energy
Pi = PI (Ratio of circumference to radius)
hbar = Planck's constant (Reduced over 2.Pi)
c = celerity, causal displacement per time interval

In most texts this is summarised as:

E = h.nu

Where:
h = Planck's constant
nu = frequency

And E is suggested to be the "total energy"And then further used to imply that it is related by:

E= hf = mc^2

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Where is gamma? Why is there no consideration for Lorentz?
How is a non-zero ground state accounted for?
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[Nugatory]

Where is gamma? Why is there no consideration for Lorentz?

Try this link for the relativistic form of these relationships: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/debrog2.html

How is a non-zero ground state accounted for?

I'm not sure I understand what you mean by "ground state" here. Can you give an example?