Precise Calculation Of Nonrelativistic Energy In PsH Systems

The main research content of this thesis is using the Rayleigh-Ritz variational method in Hylleraas coordinates to calculate the eigen energies and eigen wavefunctions of the PsH system and its isotopes(PsD?PsT),both for infinite nuclear mass and finite unclear mass.Expectations of the distances between the constituent particles are also calculated.So far,for the general three-body problem,the Schrodinger equation can be solved to very high precision using the Rayleigh-Ritz variational method in Hylleraas coordinates.For the general four-body problem,the above method can also be used,however the accuracy of the results are not as good as that of the three-body systems.But,the development of science and technology,especially the computer technology,has provided good computational resource for the high precision calculation of the four-body system.In this paper,the try to do high precision calculations to PsH and its isotopes.The main contents are as follows:In the first part,the basic theory and some specific methods of solving the Schrodinger equation of PsH and its isotopes,i.e.,the Rayleigh-Ritz variational method in Hylleraas coordinate are introduced.In this part,the main research work for us is to write the Hamiltonian matrix elements of PsH and its isotopic system in a form that suitable for programming with Fortran language,and write the matrix elements in the form of basic integral.In the second part,some useful numerical calculation skills and parallel programming techniques are introduced.First of all,the asymptotic expansion method is used to accelerate the convergence of the basic integral,and then the power method is used to solve the generalized eigenvalue of the energy.In the process of using the power method,the Cholesky decomposition of the Hamiltonian matrix element is involved.After the energy value is calculated,Newton's method is used to find the appropriate nonlinear parameters to optimize the energy value,so as to obtain the energy value with higher precision.Finally,the energy value and the corresponding nonlinear parameters are recorded.In the third part,the calculation results are given and discussed.We first give the non-relativistic energes and the expected values of the distances between the constituent particles of the PsH system with infinite nuclear mass and the PsH and its isotopes(PsD,PsT)with finite nuclear mass calculated by using the Hylleraas variational method.These results lay the foundation for the calculation of relativistic corrections and QED corrections in future.Finally,our results calculated with Hylleraas basis functions are compared with the results in literature which are calculated by using correlated Gaussian basis functions.