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In this paper, we consider Klein Gordon particle near Reissner-Nordstr\"{o}mblack hole. The symmetry of such background lead us to compare thecorresponding Laplace equation with the generalized Heun functions. Suchrelation help us achieve the generalized $sl(2)$ algebra and some suitableresults for describing the above mentioned symmetry. On the other hand in caseof $r\rightarrow r_{+}$ which is near the proximity black hole, we obtain theenergy spectrum and wave function. When we compare the equation of $R-N$background with Laguerre differential equation, we show that the obtainedenergy spectrum is same as three dimensional harmonic oscillator. So, finallywe take advantage of harmonic oscillator energy and make suitable partitionfunction. Such function help us to obtain all thermodynamical properties ofblack hole. Also, the structure of obtained entropy lead us to have some bitand information theory in the $R-N$ black hole.

Klein Gordon particle near R-N black hole, generalized sl(2) algebra and harmonic oscillator energy