We develop a simple analytic calculation for the first order wave function of helium in a model in which nuclear charge screening is caused by repulsive coulomb interaction. The perturbation term, first-order correlation energy, and first-order wave function are divided into two components, one component associated with the repulsive coulomb interaction and the other proportional to magnetic shielding. The resulting first-order wave functions are applied to calculate second-order energies within the model. We find that the second-order energies are independent of the nuclear charge screening constant in the unperturbed Hamiltonian with a central coulomb potential.

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The thermodynamics property of finite heavy mass nuclei, with the number of protons greater than the number of neutron is investigated. The core of the nucleus contains the neutron-proton pair that interacts harmonically; the excess neutron(s) reside(s) on the surface of the nucleus and introduce the anharmonic effect. The total energy is evaluated using ladder operator method and the quantum mechanical statistical expression of energy. The total energy, heat capacity and entropy are found to depend on the occupation number of states and the number of excess neutrons. At temperature near absolute zero the specific heat and entropy are lowest because a decreases in temperature leads to a decrease in particle interaction and energy.

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We consider the case of electromagnetic field inside a rectangular cavity with conducting walls as a form of a system described by classical mechanics equations. We pass these equations through the Lagrangian formalism to obtain the Hamiltonian formulation. Finally we apply canonical quantization to end up with a quantum theory of the electromagnetic field. Since classical electrodynamics can be interpreted as the quantum theory of a one photon system, then the above quantization is taken as the “quantization of the quantum theory of the electromagnetic field” or simply second quantization.