Good Quantum Numbers: Helicity & Invariants

In summary, the concept of good quantum numbers refers to the property of an operator commuting with the Hamiltonian and allowing for measurement without changing the particle's energy. While helicity is often considered a good quantum number, it is not an invariant for massive particles as it can be reversed in another Lorentz frame. However, this does not pose a problem in measuring it without changing the particle's energy. It is important to note that Dirac cautioned against assuming that helicity commutes with the quantum Hamiltonian."
  • #1
touqra
287
0
If an operator commutes with the Hamiltonian, then, the eigenvalues are said to be good quantum numbers. For example, the helicity. But then, helicity is not an invariant for a massive particle. I can always go to another Lorentz frame such that the helicity is now reversed. How then, can it be a good quantum number?
 
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  • #2
And, if you did that, the eigenvalue of the Hamiltonian, in general, would also be different; but, this doesn't seem to trouble you.

The point of thinking about "good quantum numbers" isn't that they're the same in all frames. The point is that you can measure them without changing the particle's energy.
 
  • #3
Hi touqra, I am curious where you read that helicity commutes in the quantum Hamiltonian? (Dirac warns us about that.)
 

Related to Good Quantum Numbers: Helicity & Invariants

What are Good Quantum Numbers?

Good Quantum Numbers are properties of a quantum system that are conserved and do not change over time. They are important because they allow us to describe and understand the behavior of a quantum system.

What is Helicity in Quantum Mechanics?

Helicity is a quantum number that describes the intrinsic angular momentum of a particle. It is a measure of the particle's spin in relation to its direction of motion.

What are the Invariants in Quantum Mechanics?

Invariants are physical quantities that remain unchanged under certain transformations in a quantum system. They can be used to classify and distinguish different states of a system.

Why are Helicity and Invariants considered Good Quantum Numbers?

Helicity and Invariants are considered Good Quantum Numbers because they are conserved quantities in a quantum system. This means that they do not change over time and can be used to predict and describe the behavior of a system.

How are Good Quantum Numbers used in Quantum Mechanics?

Good Quantum Numbers are used in Quantum Mechanics to classify and describe different states of a system, determine the allowed energy levels of a particle, and predict the behavior of a system over time.

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