Is Energy Truly Quantized in De Broglie's Equation?

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SUMMARY

The discussion centers on the quantization of energy as described by De Broglie's equations, specifically E = 2.Pi.hbar.c and its simplified form E = h.nu. Participants question the absence of Lorentz factors and the treatment of non-zero ground states in these equations. The implications of these relationships are further examined, particularly in relation to the total energy equation E = hf = mc^2. The conversation highlights the need for clarity on relativistic effects and the definition of ground states in quantum mechanics.

PREREQUISITES
  • Understanding of De Broglie's equations and their implications in quantum mechanics
  • Familiarity with Planck's constant and its role in energy quantization
  • Knowledge of Lorentz transformations and their significance in relativistic physics
  • Basic concepts of quantum states, particularly ground states
NEXT STEPS
  • Research the role of Lorentz factors in quantum mechanics and their relation to energy equations
  • Study the concept of ground states in quantum systems and their implications for energy quantization
  • Explore the relativistic form of De Broglie's equations and their applications in modern physics
  • Examine the relationship between frequency, energy, and mass in the context of E = mc^2
USEFUL FOR

This discussion is beneficial for physicists, students of quantum mechanics, and anyone interested in the foundational principles of energy quantization and relativistic physics.

_PJ_
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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

__________

Where is gamma? Why is there no consideration for Lorentz?
How is a non-zero ground state accounted for?
__________
 
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_PJ_ said:
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?
 

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