# What is internal state?

• I
Hi all,
I am reading some introducing materials on quantum information and quantum walk. In some materials, the author mentions to implement the related system with cold atoms and they mention the internal states. I learned the quantum mechanics some times ago but I didn't see any chapter in the text about the internal states. I wonder what is internal state really referring to. Is it other name for eigenstates?

ref: https://books.google.com/books?id=2...=what is internal state of cold atoms&f=false

https://www.cfa.harvard.edu/itamp/bec/zoller/talk.pdf [Broken]

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atyy
It is a vague, generic term usually for degrees of freedom other than the centre of mass.

http://www.phys.ens.fr/~dalibard/publi2/New-Physics.pdf
"Two types of degrees of freedom have to be considered for an atom: (i) the internal degrees of freedom, such as the electronic configuration or the spin polarization, in the center of mass reference frame; (ii) the external degrees of freedom, i.e. the position and the momentum of the center of mass."

http://www2.physics.ox.ac.uk/sites/default/files/Brandt2011.pdf
"The internal states ##|n \rangle## are the eigenstates of ##\hat{H}_{el}##"

bhobba, vanhees71 and Demystifier
Thanks. But it is still quite confusing. It looks like that the internal state is not a real quantum state to describe an atom. It is more or less like one parameter (degree of freedom) and using internal state alone is not sufficient to describe the state of atom, is that correct? I am thinking for a picture using in most text to describe the atom ##|nml\rangle##, so can I say using n or m or l alone is the internal state?

I think it is quite confusing on the second reference. There it is said ##|n\rangle## is eigenstates of ##H_{el}##, so does it mean internal state alone some times is sufficient to describe the system? Sorry, the second reference to far beyond my level to understand.

Demystifier
Gold Member
Thanks. But it is still quite confusing. It looks like that the internal state is not a real quantum state to describe an atom. It is more or less like one parameter (degree of freedom) and using internal state alone is not sufficient to describe the state of atom, is that correct?
No, internal state contains all information about the system except that "one" degree of freedom. In the case of an atom, internal state describes almost all the properties of particular electrons and their mutual correlations. The only thing that it does not contain are the few properties of the atom as a whole, like total angular momentum, total linear momentum, or position of the atom's center of mass.

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Thanks for the explanation. I am still looking for concrete example to for further explanation. I am reading some online materials, but all of them simply mention the internal state but no explanation at all. Are there any textbook has clear definition of internal state ?

Demystifier
Gold Member
Thanks for the explanation. I am still looking for concrete example to for further explanation. I am reading some online materials, but all of them simply mention the internal state but no explanation at all. Are there any textbook has clear definition of internal state ?
You can find some explanations here:
http://arxiv.org/abs/1406.3221

atyy
Thanks for the explanation. I am still looking for concrete example to for further explanation. I am reading some online materials, but all of them simply mention the internal state but no explanation at all. Are there any textbook has clear definition of internal state ?

In the simplest example of an electron, its complete state is ##|\uparrow \rangle |\Psi \rangle##. It's internal state is ##|\uparrow \rangle##.

Thanks. But it is still quite confusing. It looks like that the internal state is not a real quantum state to describe an atom. It is more or less like one parameter (degree of freedom) and using internal state alone is not sufficient to describe the state of atom, is that correct? I am thinking for a picture using in most text to describe the atom ##|nml\rangle##, so can I say using n or m or l alone is the internal state?

If you have a hydrogen atom with a spinless electron and spinless proton, then ##|nml\rangle## is the internal state (roughly, the motion of the electron around the proton). The full state must include the wave function of the centre of mass (or roughly, the motion of the proton).

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In the simplest example of an electron, its complete state is ##|\uparrow \rangle |\Psi \rangle##. It's internal state is ##|\uparrow \rangle##.
Thanks a lot. It is a good example that I understand. So rigidly, internal state is not sufficient to describe a particle, correct? But in some situation, some internal state may be ignored so the "product" of the rest internal states may be a good approximation to describe a particle?

If you have a hydrogen atom with a spinless electron and spinless proton, then ##|nml\rangle## is the internal state (roughly, the motion of the electron around the proton). The full state must include the wave function of the centre of mass (or roughly, the motion of the proton).
if spin is important, can I say spin state is one of the internal state and ##|nml\rangle## is another internal state, but either one is not sufficient to describe the atom completely, right?