Do Transition Dipole Moments Have Different Signs? Resolving a Contradiction

In summary, the electric dipole operator has odd parity, meaning it is zero for any non-degenerate ground or excited state. However, it is not zero for transitions from an excited state to a lower state of different parity. The diagonal matrix elements of the dipole operator are zero for non-degenerate states due to the even parity of the wave-functions.
  • #1
noi_tseuq
3
0
Hi,

Is dipole operator symmetric or antisimmetric? Or, in other words, do the transition dipole moments from state 1 to the state 2, and from the state 2 to the state 1 have different sign? I.e.

mu_12 = - mu_21.

As far as I understand, the diagonal elements for the dipole operator should be zero (since the transition dipole moments from state "n" to the same state "n" should ne zero). However, in this case the dipole moments of all excited states should be zeros! This does not look to be physical. How one can resolve this contradiction?

Thank you in advance.
 
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  • #2
I assume you mean the electric dipole operator, which is [tex]\vec r[/tex].
This has odd parity, so that it is zero for any non-degenerate ground or excited state.
It is not zero for transitions from an excited state to a lower state of different parity.
In any event, mu_12=mu_21.
 
  • #3
clem said:
I assume you mean the electric dipole operator, which is [tex]\vec r[/tex].
This has odd parity, so that it is zero for any non-degenerate ground or excited state.
It is not zero for transitions from an excited state to a lower state of different parity.
In any event, mu_12=mu_21.

Thank you for the answer. That what you say is an agreement with what I have. But I still does not understand the logic. You say that the dipole operator has odd party. I am not sure what exactly it means. Does it mean that the dipole operator is an odd function with respect to all Cartesian coordinates of the system? I also do not understand why in the case of the "odd parity" of the dipole operator the diagonal matrix elements should be zeros (for non-degenerate states)? Are wave-functions of non-degenerate states always even? If yes, why?

Thank you.
 
  • #4
The "parity operation" is taking each Cartesian coordinate to its negative.
This changes [tex]\vec r[/tex] to [tex]-{\vec r}[/tex].
A non-degenerate eigenstate has either even or odd parity, but then [tex|\psi|^2[/tex] will always have even parity since (-1)*(-1)=+1.
 

1. What are transition dipole moments?

Transition dipole moments are a measure of the strength and direction of the electric dipole moment between two energy states in a molecule or atom. They are important in understanding the interactions between molecules and the absorption or emission of light.

2. How do transition dipole moments have different signs?

The sign of a transition dipole moment is determined by the orientation of the electric dipole moment between two energy states. If the orientation is in the same direction, the transition dipole moment will be positive. If the orientation is in opposite directions, the transition dipole moment will be negative.

3. What contradiction is being resolved in this topic?

The contradiction being resolved is the fact that transition dipole moments can have different signs, which seems to contradict the idea that they represent the same physical quantity. This topic addresses the reasons for this contradiction and how it can be resolved.

4. How is the contradiction resolved?

The contradiction is resolved by understanding that the sign of a transition dipole moment is relative and depends on the chosen orientation of the electric dipole moment. By using a consistent orientation convention, the apparent contradiction can be resolved.

5. Why is understanding transition dipole moments important?

Understanding transition dipole moments is important in various fields of science, including chemistry, physics, and materials science. They provide valuable information about the electronic structure and interactions of molecules and atoms, and are crucial in explaining phenomena such as absorption and emission spectra.

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