Why do probabilities distinguish between multiplet states?

In summary, the strong interactions are assumed to have isospin invariance, which means that the probabilities and cross sections for these interactions are given by the appropriate SU(2) Clebsch-Gordan coefficients. However, the probabilities still depend on the third component of isospin, even if it is an exact symmetry. This is because electric charge also needs to be conserved in addition to isospin.
  • #1
metroplex021
151
0
I'm pretty sure the answer to this will be more than obvious, but I've been wondering about the following.

Isospin invariance is assumed to be an (approximate) symmetry of the strong interactions. Ratios of cross sections for strong interactions are then given by the appropriate SU(2) Clebsch-Gordan coefficients. These coefficients depend on the third component of isospin of the particles involved; hence the probabilities and cross sections for strong interactions do too. But if isospin is a symmetry of the strong interactions (and let's assume for simplicity it is an exact symmetry), why should probabilities of strong processes depend on the third component of isospin? Since isospin symmetry means (roughly!) that the strong interaction doesn't 'see' any differences between the members of an isospin multiplet, why should the probabilities of strong processes vary depending on which members of a given multiplet are involved?
 
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  • #2
Because electric charge needs to be conserved as well.
 

FAQ: Why do probabilities distinguish between multiplet states?

1. Why do different multiplet states have different probabilities?

The probabilities of different multiplet states depend on the quantum numbers associated with each state. These quantum numbers determine the energy levels and spatial orientations of the electrons in the system, which in turn affect the probability of finding an electron in a particular state.

2. How do probabilities distinguish between multiplet states?

Probabilities distinguish between multiplet states by assigning different likelihoods of finding an electron in each state. This is based on the different energy levels and spatial orientations associated with each state, which affects the probability of an electron occupying that state.

3. What is the significance of multiplet states in probability calculations?

Multiplet states are important in probability calculations because they provide information about the spatial and energy distribution of electrons in a system. By understanding the probabilities associated with different multiplet states, scientists can make predictions about the behavior and properties of a system.

4. Can probabilities of multiplet states change over time?

Yes, probabilities of multiplet states can change over time. This is because the energy levels and spatial orientations of electrons can change due to external influences, such as temperature or applied electric or magnetic fields. These changes can affect the probabilities of electrons occupying different multiplet states.

5. How do multiplet states relate to the concept of quantum mechanics?

Multiplet states are a fundamental concept in quantum mechanics. They represent the different possible states that an electron can occupy in a system, based on its energy and spatial properties. The probabilities associated with these states are described by quantum mechanics equations, and understanding these probabilities is essential for predicting the behavior of quantum systems.

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