Estimate calculation of discrete energy levels in the hydrogen atom using an indeterministic method

Abstract

In the present study, we use the indeterministic method based on uncertainty conditions to estimate the discrete energy levels of hydrogen atoms. We analyze in detail how transitions from the ground state (n = 1) to the first excited state (n = 2) occur by dividing into sub-states and introducing the indeterminacy concept. The calculated energy levels expressed that as the indeterminacy changes, the energy level increases from -13.60 eV to -3.40 eV and there is observed a decrease in energy required to transition from each sub-state to n = 2. Such as for the transition from n = 1.1 to n = 2.0 there is a need for 9.18 eV. As a result, it is found that our new approach exploits the uncertainty principle to reveal deep trends in the energy transition. This work has significant implications for atomic physics and energy applications, spectroscopy and quantum mechanics. Our findings demonstrate the potential of imprecise data to contribute significantly to scientific understanding.