In this paper, a theoretical study of the energy spectra and the heat capacity of one electron quantum dot with Gaussian Confinement in an external magnetic field are presented. Using the exact diagonalization technique, the Hamiltonian of the Gaussian Quantum Dot (GQD) including the electron spin is solved. All the elements in the energy matrix are found in closed form. The eigenenergies of the electron were displayed as a function of magnetic field, Gaussian confinement potential depth and quantum dot size. Explanations to the behavior of the quantum dot heat capacity curve, as a function of external applied magnetic field and temperature, are presented.

The aim of this work is to calculate the one- electron expectation value of the electronic charge of atomic system Z=2,3….7 and we compare with He atom . the electronic density function D(r1) of He atom and like ions are evaluated . using Hartree –Fock wave.

Magnetic resonance cholangiopancreatography (MRCP) is a non-invasive imaging test with excellent overall sensitivity and specificity for demonstrating the level and the presence of a biliary obstruction. MRCP has emerged as an accurate, diagnostic modality for investigating the biliary and pancreatic duct. In some cases, it has been recommended that preoperative MRCP is a good choice for the detection of CBD stones.