What is V-representable and how is it used?

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In summary, "V-representable" refers to a particle-density distribution that is the ground-state density for a potential, as defined in an abstract of a physics article. It is distinct from topics in linear and abstract algebra.
  • #1
kof9595995
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what's "V-representable"

Just encountered this word, not sure what it means. I tried google and wiki, but didn't find any introductory articles, only some professional articles which mentioned this word.
Can someone introduce a bit?
P.S. I'm not even sure where to post question, for I haven't figured out whether it's more mathematical or physical, so I put it here, randomly.
 
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  • #2


Perhaps some context would be useful...
 
  • #3


As rochfor1 says, we really need to know the context.

Until then I would guess that you are saying that group G has a representation as a group of linear transformations from vector space V to itself.
 
  • #4


HallsofIvy said:
As rochfor1 says, we really need to know the context.

Until then I would guess that you are saying that group G has a representation as a group of linear transformations from vector space V to itself.

I think V refers to potential, I only found a definition(sort of, not quite formal) from an abstract of a article:
http://pra.aps.org/abstract/PRA/v47/i1/p153_1
"A particle-density distribution is said to be v-representable if it is the ground-state density for some potential v(r)"
And I don't understand it.
 
  • #5


Then this has nothing to do with "Linear and Abstract Algebra"! In fact, it sounds like it is physics rather than mathematics.
 

1. What does "V-representable" mean in the context of science?

"V-representable" refers to a mathematical concept used in quantum chemistry and physics. It describes the ability to represent a function as a linear combination of basis functions, where the coefficients of the linear combination depend on the coordinates of the system.

2. How is "V-representable" related to the electronic structure of atoms and molecules?

In the context of electronic structure calculations, "V-representable" means that the many-electron wave function can be expressed as a linear combination of Slater determinants, which are constructed from a set of single-particle orbitals.

3. What is the significance of a system being "V-representable"?

A system being "V-representable" is important because it allows for efficient and accurate calculations of electronic structure, which is crucial for understanding the properties and behavior of atoms and molecules.

4. Can all systems be described as "V-representable"?

No, not all systems can be described as "V-representable." In some cases, the wave function cannot be expressed as a linear combination of basis functions, making the system non-"V-representable." This is often the case for highly correlated systems or systems with strong electron-electron interactions.

5. How is the concept of "V-representable" used in practical applications?

The concept of "V-representable" is used in a variety of practical applications, such as in computational chemistry software to accurately predict the electronic structure of molecules. It is also used in theoretical studies to understand the behavior of complex systems and in developing new methods for electronic structure calculations.

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