“QUANTUM ANALYSIS OF THE HYDROGEN ATOM: WAVE FUNCTIONS AND RADIAL PROBABILITY DISTRIBUTIONS OF 1S AND 2S STATES” - Kuchkarov M.Kh; Aliyev Kh.F (Ta’lim innovatsiyasi va integratsiyasi, 2025)
Abstract: This article analyzes the wave functions corresponding to the 1s and 2s quantum states of the hydrogen atom. For the ground (1s) state, the wave function, probability density, and radial probability function are presented on a mathematical basis, and their physical meaning is explained in detail. Additionally, the most probable radius and the average distance of the electron are determined and compared with the results from the Bohr theory. For the 2s state, the wave function and the graph of the radial probability density are studied, demonstrating that the electron in this state is located, on average, much farther from the nucleus. The results show the intrinsic connection between quantum mechanics and the Bohr model.