Quantum confinement effect in semiconductor quantum dots (QD's) of CdSe, ZnS and GaAs has been studied using the Brus Equation. It is found that the simple models obtained for the three different semiconductor nanocrystals exhibit the size dependence predicted by the particle-in-a-box model. The result shows that ground state confinement energy is inversely proportional to the size (radius). Thus, as one increases the radius (size), the confinement energy decreases, but never reaches zero. i.e., the lowest possible energy for the quantum dot sample is not zero.

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In this paper, the energy spectra of the general molecular potential are obtained using the asymptotic iteration method within the framework of non-relativistic quantum mechanics.With the energy spectrum obtained, the vibrational partition function is calculated in a closed form and is used to obtain an expression for other thermodynamic functions such as vibrational mean energy U , vibrational mean free energy F, vibrational entropy S and vibrational specific heat capacity C. These thermodynamic functions are studied for the electronic state X 1 + g of K 2 diatomic molecules.

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