Confirming the Correlation of Quantum States and Lowest Quantum Numbers

[lion8172]

Is it generally true that the ground state of a given quantum system corresponds to the lowest quantum numbers? If so, how do we know this?

 

[Marco_84]

Is it generally true that the ground state of a given quantum system corresponds to the lowest quantum numbers? If so, how do we know this?

When dealing with quantum systems (classical also) it is common to classify their states looking up their simmetries. When you do this you are actually using a group, or better a specific group representattion on a hilbert space which gives back to you a basis classified with labels that you can call "quantum numbers".

Now it is just a matter of convention to classify the basis functions from the trival one to the more complicated increasing the label (think about the spherical armonics for an example).
Usually the ground state of a "simple" system is described by "simple" wavefunctions.

I hope i answered to you.

marco

 

[denian]

Yes, it is generally true that the ground state of a given quantum system corresponds to the lowest quantum numbers. This is known as the Pauli exclusion principle, which states that no two electrons in an atom can have the same set of quantum numbers. Therefore, the ground state, which is the state of lowest energy, will have the lowest possible quantum numbers.

This principle has been confirmed through numerous experiments and observations in quantum mechanics. For example, the electron configuration of atoms can be determined using spectroscopic techniques, and it has been consistently found that the ground state corresponds to the lowest possible quantum numbers.

Additionally, theoretical calculations and models in quantum mechanics also support the idea that the ground state corresponds to the lowest quantum numbers. The Schrödinger equation, which describes the behavior of quantum systems, predicts that the lowest energy state will have the lowest quantum numbers.

Overall, the consistency of experimental observations and theoretical predictions support the general truth that the ground state of a given quantum system corresponds to the lowest quantum numbers.