CALCULATION OF THE ENERGY-LEVELS OF A HYDROGEN-ATOM IN A MAGNETIC-FIELD OF ARBITRARY STRENGTH BY USING B-SPLINES

B splines with carefully adjusted knot sequences are used as basis fun ctions in cylindrical coordinates to calculate the energy levels of th e low-lying (m = 0) states of a hydrogen atom in a uniform magnetic fi eld of arbitrary strength by using the variational method. The strengt h of the held calculated covers a range from gamma = 0 to gamma = 100 000 for the ground state and up to gamma = 2000 for the 2s and 2p stat es. A precision of up to ten digits in the region of 0 less than or eq ual to gamma less than or equal to 200 and up to eight digits for gamm a > 200 has been maintained for all the results presented. In order to test the applicability of the B splines for the higher excited states , the energy levels of 3s, 3p, 3d, and 4f states with m = 0 in the fie ld region of 0 less than or equal to gamma less than or equal to 10 ha ve also been calculated. Even though the number of basis sets was kept constant, the accuracy of the results was maintained in the intermedi ate field regions and also in the very strong field regions, which are known to be difficult for achieving high accuracy. The flexibility of the B splines is demonstrated here by the uniformly accurate results in the transition from spherical symmetry to Landau symmetry as the fi eld strength of the magnetic field is increased. The energy levels of all the low-lying states with various ranges of magnetic field strengt h have been compared with published values. They are in good agreement with the most updated values and compare favorably with all other pub lished results.