Can the Energy for Non-Integer Values be Modeled in a Quantum System?

[eljose]

Let,s suppose we have a qunatum system so the energies are the roots of the function f(x)=0..then my question is that we could calculate the roots to obtain E(0),E(1),E(2),...but the problem comes when we have the integral..

$$\int_0^{\infty}E(n)dn$$ my question is if for this case we could modelize E(n) for non-integer n in the form:

$$E(n)=\sum_{k=0}^{\infty}E(n)\delta(n-k)$$

so for this case the sum becomse the series: $$\sum_{k}E(k)$$ for every positive integer... thanx.

 

[solidspin]

We use density matrices all the time w/r/t our pulse sequences in solid-state NMR. They're extremely powerful from a practical pov, b/z the off-diagonal terms represent coherences w/ very useful physical meaning.

A reasonable book w/ some very good practical application is called Spin Dynamics, by Malcolm Levitt. Of course, this is about NMR, but you will quickly see that manipulation of large nxn matrices, after some manipulation of sandwich operators, yields some great results w/o too much headscratching.