Excited states and selection rules

In summary, excited states in atoms are energy levels that electrons occupy when they have absorbed energy. They are related to an atom's emission spectrum as the excess energy is released in the form of light. Selection rules in spectroscopy govern which transitions are allowed or forbidden based on energy, angular momentum, and parity conservation. These rules can be violated under certain circumstances, leading to the emission of unexpected light. In quantum mechanics, selection rules are used to determine the probability of transitions and provide insights into electronic structure.
  • #1
Gregg
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If you have a meson in the states

## ^3S_1## and ## ^1S_0 ## this means that ##J^P = 1^+ ## and ## 0^+## doesn't it?

But if you have excited states

## ^1P_1 ## this is ##J^P=1^- ## but isn't ## ^3P_1 ## supposed to be ##J^P = 1^- ##? Does this matter?

##^3P_0##, ##^3P_1## and ##^3P_2## for the triplet with ## |L-S| \le J \le L+S ## what are the values ##J=0,1,2## referring to physically. ##L## is the orbital angular moment of the two quarks, and S is their spin, so for them to couple in a way that gives ##J=2## what does that mean?
 
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  • #2
Yes, the notation ##^3S_1## and ##^1S_0## refer to states with angular momentum quantum numbers ##J^P = 1^+ ## and ##0^+## respectively. For an excited state such as ##^1P_1##, the quantum numbers are ##J^P=1^-##.The quantum numbers ##J^P## for an excited triplet state such as ##^3P_1## refer to the total angular momentum and parity of the system. In particular, ##J## is the total angular momentum quantum number, and ##P## is the parity quantum number. The possible values of ##J## and ##P## depend on the angular momentum and spin of the two quarks forming the meson. Specifically, the angular momentum quantum number ##L## refers to the orbital angular momentum of the two quarks, and ##S## is their spin. The relation between these two and the total angular momentum quantum number is given by the equation: ## |L-S| \le J \le L+S ##. This means that for the triplet states ##^3P_0##, ##^3P_1## and ##^3P_2##, the values of ##J## represent 0, 1, and 2 respectively. Physically, this means that the two quarks have an orbital angular momentum of 1 and a spin of 1, and that they can couple together in such a way that the total angular momentum has a magnitude of 0, 1, or 2 depending on the relative orientation of the two spins.
 

1. What are excited states in atoms?

Excited states in atoms refer to the energy levels that electrons occupy when they have absorbed energy and moved to a higher energy level. This energy can come from various sources such as heat, light, or electricity.

2. How are excited states related to an atom's emission spectrum?

When an atom in an excited state returns to its ground state, it releases the excess energy in the form of light. This light is specific to the element and its excited state, leading to the unique emission spectrum of each element.

3. What are selection rules in spectroscopy?

Selection rules in spectroscopy refer to the rules that govern which transitions between energy levels are allowed or forbidden. These rules are based on the conservation of energy, angular momentum, and parity.

4. Can selection rules be violated?

Yes, selection rules can be violated under certain circumstances, such as when there is a high energy or intense electric field present. This can cause forbidden transitions to occur, leading to the emission of light that would not typically be observed.

5. How are selection rules used in quantum mechanics?

In quantum mechanics, selection rules are used to determine the probability of a transition between energy levels based on the allowed or forbidden nature of the transition. They help to explain the observed spectral lines and provide insights into the electronic structure of atoms and molecules.

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