# Calculate energy level spectra?

1. Mar 30, 2009

### xylai

Recently, I read one book about quantum chaos. In it, random-matrix theory is used to describe the quantum signatures of chaos.
Firstly, a new set of levels {E’1,E’2,E’3,...} is gained by unfolding the vibrational spectrum {E1,E2,E3,...}:

$$E'_{i+1}=E'_{i}+(2k+1)\frac{E_{i+1}-E_{i}}{E_{j2+1}-E_{j1}}$$,
where $$j1=i-k,j2=i+k$$. Let k=3.

Secondly, the probability distribution of the nearest-neighbor level spacings P(s) of the unfolded spectrum is calculated.

Here, I want to know how to calculate P(s)?

In the following, I will show how I calculate the P(s). Maybe it is wrong.
(1) I unfold the vibrational spectrum {E1,E2,E3,...} and let E’1=0.
(2) I count how many levels in the energy interval {0-ds},{ds-2ds},{2ds-3ds},…, respectively. Then I obtain P(s).