Calculation On The Confined Atoms And Molecules

In this thesis, we summaries two aspects of my research e?orts obtained with theFORTRAN Language programs as follows:1,Since the beginning of last century,physicists as well as chemists made a lot of e?ortsto study the quantum objects confined by di?erent forms of external potentials.What'smore, the recent breakthrough in semiconductor technology such as the quantum wells(QW), quantum-well wires (QWW), and quantum dots (QD)bring more attentions to thisarea and advance the pure theoretical work in to the potential application .The quantumlow dimensional the impurity e?ected in can be seen as a confined 2D hydrogen atomfrom the atomic physicists side.To explain the experiment spectra and its own propertiesof the o? center problem,attracts research interests.The o? center problem will lead theSchr¨odinger equation unable to separate the variable,the ordinary perturbation methodfails to work.However the B-spline method can solve the di?culty successfully.Applying the B-spline method to calculate the energy of two dimensional hydrogenatom and hydrogen molecular ion.For the on center hydrogen atom,we get high precisionresults better than the reference paper. For the o? center hydrogen atom,we gave thequantitative explanation about the relationship between o? center distance and theenergy under di?erent confined distance.we also calculate the nuclear separation and theenergy of Hydrogen molecular ion and obtained their quantitative relationship.2,The hyperspherical coordinate has long and successful history dealing with the 3-body system,especially coulomb 3-body system for its advantages such as irrelevantto the mass of particle. However, the traditional method has two problems.One is thelocalization of wavefunction at large hyper radius. The other is solve the hyper-radiuscoupling di?erential equation.To overcome these two di?culties,we combine the B-splinemethod and the discrete variable representation.Applying the special feature of the B-spline function like the localization and ?exibility we obtains a highly accurate hyperradius potential and the channel function by modifying the knots distribution of theB-spline basis. Instead of solve the hyper-radius coupling di?erential equation; we trans-form it into a hyper-radius generalized algebraic eigenvalue problem by discrete variablerepresentation. Therefore we successfully reduce the calculation expense and improvethe precision and stabilization for numerical calculation, overcome the defects of ordi-nary method such as: low precision and the giant calculation expense, which is causedby direct solving the hyper-radius coupling di?erential equation. We obtain the weaklybound ground states of the typical three body coulomb system: hydride ion with theimproved hyperspherical method mentioned above. We achieved high accurate results of8 digits precision, which is one of most accurate results of the hyperspherical coordinateup to now.