A variational principle is applied to the Schroedinger equation for theXY₂ linear molecule. Trial solutions are synthesized from the nuclear eigenstates, which are assumed to be simple harmonic oscillator eigenstates, and from the unperturbed electronic states, whose azimuthal dependence is known because of the cylindrical symmetry of the field of the nuclei. The secular equation is discussed, and an expression for the Renner splitting of the π state is obtained. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

In studying the diamagnetism of free electrons in a uniform magnetic field it was found that reducing the field to zero in the wavefunction did not yield the experimentally indicated free particle plane wave wavefunction. However, solving the Schroedinger Equation resulting from setting the field equal to zero in the original equation did yield a plane wave wavefunction. This paradox was not found to be peculiar to the case of a charged particle in a uniform magnetic field but was found to occur in a number of other systems. In order to gain an understanding of this unexpected behavior, the following systems were analyzed: the one-dimensional square well potential; a charged, spinless particle in a Coulomb field and in a uniform electric field; a one-dimensional harmonic oscillator; and a charged, spinless particle in a uniform magnetic field. From these studies the following were obtained: conditions for determining the result of reducing the potential in a wavefunction; the condition under which the potential of a system may be switched off while maintaining the energy of the system constant; the relationship between the result of physically switching off a potential, the result of reducing it in the wavefunction, and the solution of the Schroedinger Equation obtained by decreasing the potential to zero in the original wave equation; and a general property of any wavefunction with respect to reducing any parameter within this wavefunction. / Science, Faculty of / Physics and Astronomy, Department of / Graduate