The Quantum States of a Hydrogen Atom nearby Hyperboloid Surfaces of Revolution with Impenetrable Walls

• Main Authors: Kuo Chang-tay, 郭忠泰
• Other Authors: Yang Chi
• Format: Others
• Language: zh-TW
• Published: 1993
• Online Access: http://ndltd.ncl.edu.tw/handle/25408812704044407703

碩士 === 淡江大學 === 物理研究所 === 81 === Consider a hydrogenic system that hyperboliod surfaces of revolution with impenetrable walls for electrons are boundary surfaces. In prolate spheroidal coordinate system, we derived the electron wavefunctions from the Schrodinger equation. Then from the following conditions, the boundary condition and the wavefunctions cannot be equal to zero everywhere in all space to find the energy eigenvalues and separate constants of this system. Normalize the wavefunctions that we had obtained, in order to evaluate physical quantities that we need, for example the electron probability density at the nucleus, dipole moment, nuclear magnetic shielding and polarizality. Draw out the diagrams each physical quantity versus distance and the planar equivalence diagram of the electron probability density. From the wavefunctions in the limiting case of xy plane we obatined that we can realize the probable shapes of these planar equivalence diagrams. From the figures energy versus distance, we found if there are some convexitits on a surface when some atom approaches the surface that this atom has larger probability to attach the convexitity because this atom has lower energy in the convexitity than in the concavity. This phenomenon likes crystal growth. From the figures dipole moment versus distance, diamagnetic screening constant versus distance, polarizality versus distance and the electron probability density at the nucleus versus distance, we can look out the varieties of these physical quantities and explore the varing reasons of these ones. If the distance from the atom to the top of hyperboloid surfaces of revolution is unchanged but the shape of boundary surfaces and the distance from the atom to xy plane have changed, from these figures we can look out the varieties of these physical quantities to understand the qulitity of these ones under these boundary surfaces.