Abstract
We discuss the quantum mechanics of many-body systems, that is, hybrid microgel consisting of negatively charged anionic microgels possessing thick sheath of water molecules solvating protruding anionic moieties and nanoparticle captivated within the microgel. Thermodynamic feasibility of synthesis of particular nanoparticle within the microgel is dependent upon the magnitude of interaction between nanoparticle, water molecules, and microgel relative to sum of magnitude of self-interaction between counterions and interaction between counterions and microgel. Nanoparticles synthesized with in the microgels have thick electronic cloud that oscillates under the influence of net interaction potential of charged anionic moieties and solvent water molecules which constitutes the chemical environment of hybrid microgel. Hamiltonian describing energy of oscillating electronic cloud of wrapped around nanoparticle is mathematically derived to be equal to product of integral electron density and product of its position vector overall space and net force acting on the oscillating electronic cloud of nanoparticle is mathematically defined as; ℱ∫ρn{n}n^ dn.
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