a numerical renormalization group approach for calculating the spectrum of a vibronic system occurring in molecules or impurities in insulators

theoretically, in order to describe the behavior of a spectrum, a mathematical model whichcould predict the spectrum characteristics is needed. since in this study a two-state system has beenused like models which was introduced previously past and could couple with the environment, theformer ideas have been extended in this study. we use the second quantized version for writing thishamiltonian. first, the hamiltonian of a rotational system is considered in a classic scale,afterwards it is brought to a quantum scale. in the first step, the vibrations and quantum rotation isillustrated for two atom molecules. then it is devoted to two-state system and dissipative twostatesystem.in the second step, the rotation of a molecular group in a hindering potential is studied in theclassic and quantum scales. finally, at the present of strong coupling constant the hamiltonian hasbeen applied and a numerical renormalization group approach has been used for numerical solution.then, by using hubbard operators, dynamical functions of this oprators are written. the fouriertransform of the greens function is developed, then density of state is calculated.