A new theoretical approach has been adopted to calculate the non-relativistic parity conserved two-photon transition probability (TPTP) from ground to excited S and D states along with the hyperfine splitting (HFS) of ground and excited S states of H atom within principal quantum number $n\le 4$ under classical and quantum plasma environment represented by screened potential model. The methodology involves direct calculation of TPTP via an intermediate virtual state obtained from time dependent variation perturbation formalism. The standard formula with sum over states representing the TPTP has been replaced by its variational equivalent obtained from currently established procedure for two-photon excitation via fourth order time dependent variation perturbation theory. Unlike previous methodologies the current formalism yields a compact representation of the physical nature of the intermediate virtual state having well defined profile. The HFS has been evaluated under first order perturbation theory. The plasma embedded ground state energy is obtained from standard diagonalization procedure. Finite Slater type basis sets have been used for the ground and all the excited states. The variational coefficients for the excited states are determined from optimization of an appropriate time averaged variational functional. Results for free H atom agree well with existing estimates for all the states. The results for the plasma embedded states follow smooth and interesting pattern.

采用了一种新的理论方法来计算从基态到激发态S和D的非相对论奇偶性守恒双光子跃迁概率（TPTP）以及主原子内H原子的激发态和S态的超精细分裂（HFS）量子数 $ñ\le 4$在经典和量子等离子体环境下，由筛选势模型表示。该方法涉及通过从依赖于时间的变化扰动形式主义获得的中间虚拟状态来直接计算TPTP。具有代表TPTP的状态总和的标准公式已被其变分等效项所取代，该变项等效项是通过四阶时间相关的变化扰动理论从当前建立的用于双光子激发的过程中获得的。与以前的方法不同，当前的形式主义产生了具有明确定义的轮廓的中间虚拟状态的物理性质的紧凑表示。HFS已根据一阶扰动理论进行了评估。等离子体嵌入的基态能量是从标准对角化过程中获得的。有限Slater类型基集已用于基态和所有激发态。激发态的变分系数由适当的时间平均变分函数的优化确定。游离H原子的结果与所有州的现有估计非常吻合。等离子体嵌入状态的结果遵循平滑有趣的模式。