Quantum Mechanical Operators - A Question Or Two

In summary, the conversation discusses whether mass is quantized, with the conclusion that it is not necessarily quantized and is gained through interaction with the Higgs field. The conversation also mentions the existence of an operator associated with mass, which is a scalar.
  • #1
dweeegs
12
1
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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  • #2
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
 

Related to Quantum Mechanical Operators - A Question Or Two

1. What are quantum mechanical operators?

Quantum mechanical operators are mathematical representations of physical observables in quantum mechanics. They are used to describe the behavior and properties of quantum systems, such as the position, momentum, and energy of particles.

2. How do quantum mechanical operators work?

Quantum mechanical operators operate on quantum states, which are represented by mathematical objects known as wave functions. When an operator acts on a wave function, it produces a new wave function that describes the state of the system after the measurement of the corresponding observable.

3. What is the significance of quantum mechanical operators?

Quantum mechanical operators are essential in quantum mechanics because they allow us to make predictions about the behavior of quantum systems. They also play a crucial role in the formulation of the famous Schrodinger equation, which describes the time evolution of quantum systems.

4. How are quantum mechanical operators related to uncertainty principle?

The uncertainty principle states that it is impossible to simultaneously know the exact values of certain pairs of observables, such as position and momentum. Quantum mechanical operators represent these observables, and the mathematical operations involved in measuring them inherently contribute to the uncertainty principle.

5. Are there different types of quantum mechanical operators?

Yes, there are several types of quantum mechanical operators, including position operators, momentum operators, angular momentum operators, and energy operators. Each type of operator corresponds to a different observable in quantum mechanics.

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