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