Odd Parity of States: 2p m=0, 2p m=1, 26f m=0, 2s

In summary, the conversation discusses the odd parity of various states, specifically a 2p m=0, b 2p m=1, c 26f m=0, and d 2s. The speaker suggests determining the wavefunctions for each state and using them to understand the behavior under a parity transformation. This leads to a discussion of the form of the wavefunction and its components such as n, m, and l.
  • #1
Mattofix
138
0

Homework Statement



Which of the following states have odd parity?

a. 2p m=0
b. 2p m=1
c. 26f m=0
d. 2s


The Attempt at a Solution



Knowing the wavefunctions for a,b, and d, i think that all of them have odd parity. What about the 26f m=0 state?
 
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  • #2
I'd recommend you write down the values of [itex]n[/itex], [itex]m[/itex] and [itex]\ell[/itex] for each of those orbitals, and then use those to deduce the form of each wavefunction, and then see what happens to each one under the parity transformation.

[tex] \psi_{n\ell m}(r,\vartheta,\varphi) \propto e^{- \rho / 2} \rho^{\ell} L_{n-\ell-1}^{2\ell+1}(\rho) \cdot Y_{\ell}^{m}(\vartheta, \varphi ) [/tex]
 

1. What is odd parity of states?

Odd parity of states refers to the quantum mechanical property of a state having a negative intrinsic parity value. This means that the wavefunction of the state changes sign under inversion, or a reflection through the origin. This is in contrast to even parity states, which have a positive intrinsic parity value.

2. What is the significance of 2p m=0, 2p m=1, 26f m=0, 2s in odd parity states?

These are specific examples of states with odd parity. The numbers and letters represent the orbital angular momentum and magnetic quantum numbers, respectively. The 2p and 2s states have an angular momentum value of 1 and 0, respectively, while the 26f state has a higher angular momentum value of 3. The m values indicate the orientation of the angular momentum vector in space.

3. How are odd parity states determined experimentally?

Odd parity states can be determined experimentally through spectroscopy, which involves studying the interactions between electromagnetic radiation and matter. The energy levels and transitions of atoms and molecules can reveal the parity of the states. Additionally, parity can also be determined through scattering experiments.

4. What is the role of odd parity states in atomic and molecular physics?

Odd parity states play a significant role in understanding the properties and behavior of atoms and molecules. They can impact the stability and reactivity of molecules, as well as the selection rules for transitions between energy levels. In atomic physics, odd parity states can also affect the polarization of light emitted or absorbed by atoms.

5. Can odd parity states have other quantum numbers besides angular momentum and magnetic quantum numbers?

Yes, odd parity states can have other quantum numbers such as spin, total angular momentum, and isospin. These additional quantum numbers can further differentiate between different states and provide more information about their properties and behavior.

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