Quantum Mechanical Operators - A Question Or Two

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SUMMARY

Mass is not inherently quantized, despite energy and momentum being quantized in quantum mechanics. The discussion centers around the relationship between mass, energy, and momentum, particularly through the equation E² = (pc)² + (mc²)². While energy can be quantized, especially in bound systems, free particles do not exhibit quantized energy levels. Additionally, there is indeed a scalar operator associated with mass, confirming its role in quantum mechanics.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with the concepts of energy and momentum operators
  • Knowledge of the Higgs field and its role in mass generation
  • Basic grasp of eigenvalues and eigenstates in quantum theory
NEXT STEPS
  • Study the implications of the Higgs mechanism on particle mass
  • Explore the role of scalar operators in quantum mechanics
  • Investigate the quantization of energy in bound versus free systems
  • Learn about the mathematical formulation of quantum mechanical operators
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Students and researchers in physics, particularly those focusing on quantum mechanics, particle physics, and the theoretical underpinnings of mass and energy interactions.

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A couple questions: is mass quantized? Energy is quantized, and momentum has eigenvalues for its operator so I took that to mean that momentum is also quantized.

If those two are true (might not be! I'm new to this :-p), following

E^2 = (pc)^2 + (mc^2)^2

Would that not mean that mass is also quantized?

And the actual question I wanted to ask:

Is there an operator associated with mass?
 
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Energy is not necessarily quantised eg a free particle does not have energy quantised. Mass is gained by interaction with the Higgs field, but I am not expert enough in the theory to know if it implies mass is quantised - I don't think it does - but don't know the details well enough to be sure.

And yes there is an operator associated with mass - its a scalar.

Thanks
Bill
 

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