  In this work, we obtained analytical bound state solution of the
Schr\"odinger equation with Manning Rosen plus exponential Yukawa Potential
using parametric Nikiforov-Uvarov method (NU). We obtained the normalized wave
function in terms of Jacobi polynomial. The energy eigen equation was
determined and presented in a compact form. The study also includes the
computations of partition function and other thermodynamics properties such as
vibrational mean energy ({\mu}), vibrational heat capacity (c), vibrational
entropy (s) and vibrational free energy (F). Using a well design maple
programme, we obtained numerical bound state energies for different quantum
states with various screening parameters: {\alpha}=0.1,0.2,0.3,0.4 and 0.5. The
numerical results showed that the bound state energies increase with an
increase in quantum state while the thermodynamic plots were in excellent
agreement to work of existing literature.
