Quantum Mechanical Operators - A Question Or Two

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dweeegs
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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