Scaling rule, energy distribution and energy level analysis for morse oscillator by virtue of Hermann-Feynman theorem

We propose the scaling rule of Morse oscillator, based on this rule and by virtue of the Hermann-Feymann theorem, we respectively obtain the distribution of potential and kinetic energy of the Morse Hamiltonian. Also, we derive the exact upper limit of physical energy level. Further, we derive some recursive relations for energy matrix elements of the potential and other similar operators in the context of Morse oscillator theory.