The meaning (and validity) of fractional occupations in QM

In summary, there is a debate in the scientific community, specifically between chemists and physicists, about solutions to equations that result in fractional occupations of molecular or KS orbitals. The speaker sees no issue with this and believes it can lead to lower energy solutions. They ask if this violates any key properties of quantum mechanics. The person responding is a quantum chemist and is unfamiliar with this disagreement and does not see it as a problem. They also question the expectation of integer occupancies in an interacting Hamiltonian.
  • #1
Einstein Mcfly
162
3
Hello all. As I understand it, there's somewhat of a divide in the scientific community (basically between chemists and physicist) around the topic of solutions to the SE (or KS eqn) that give fractional occupations of molecular or KS orbitals. I myself see no physical reason why probability can't be allowed to leak into a number of orbitals in quantities less than one, particularly if it gives a lower energy solution. Is there anything that I should understand in this regard (ie, that these solutions violate some key property of QM such as <S**2> not being a good quantum #)?

Thanks for your thoughts.
 
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  • #2
I'm a quantum chemist, and this is the first I've ever heard of such a thing. (Or indeed any kind of fundamental disagreement between chemists and physicists.)

You'll have to elaborate on what you mean; I don't see the problem. On the contrary, I don't know why anyone would expect integer occupancies for an interacting Hamiltonian in a single-particle basis.
 

FAQ: The meaning (and validity) of fractional occupations in QM

What is the concept of fractional occupations in quantum mechanics?

Fractional occupations in quantum mechanics refer to the idea that in certain quantum systems, particles can occupy a state with a fraction of the total probability. This means that a particle can exist in a state with a probability less than 1, unlike in classical mechanics where a particle can only exist in one state at a time.

How are fractional occupations calculated in quantum mechanics?

Fractional occupations are calculated using the density matrix formalism in quantum mechanics. The density matrix, also known as the density operator, is a mathematical tool that describes the statistical state of a quantum system. It contains information about the probabilities of a system being in different states, including fractional probabilities.

What is the significance of fractional occupations in quantum mechanics?

Fractional occupations have important implications in understanding the behavior of quantum systems. They can provide insight into the distribution and flow of energy in a system, and can also affect the properties of materials at the atomic level. Additionally, fractional occupations are essential in accurately describing complex quantum phenomena such as superposition and entanglement.

Are fractional occupations in quantum mechanics valid?

Yes, fractional occupations are a valid concept in quantum mechanics. They are a natural consequence of the probabilistic nature of quantum systems and have been experimentally observed in various systems. Additionally, fractional occupations are mathematically consistent and have been successfully used in a variety of theoretical models.

What are some common misconceptions about fractional occupations in quantum mechanics?

One common misconception is that fractional occupations imply that particles can exist in two states simultaneously, similar to the concept of superposition. However, fractional occupations do not necessarily mean that a particle exists in multiple states at once, but rather that it has a certain probability of being in each state. Another misconception is that fractional occupations violate the principle of conservation of energy, but this is not the case as the total probability of a particle is always conserved.

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