The Many-Worlds Interpretation versus the Copenhagen Interpretation: A Case Discussion with the Hydrogen Atom

Abstract: The main objective of this work is to compare the interpretations of the hydrogen atom spectrum according to two famous schools in quantum mechanics: Copenhagen and many-worlds. The Schrodinger equation is solved using the many-worlds interpretation, and the results are then compared to those obtained using the Copenhagen interpretation. While the energy spectra are similar in both cases, the interpretations of these results differ. In the many-worlds interpretation, the eigenvectors are entangled across multiple worlds, whereas, in the Copenhagen interpretation, they are superimposed. The hydrogen atom, being a system of only one electron and without electron-electron interaction, serves as a clear and accessible example for comparing these interpretations. In this case, the wave function depends on independent coordinates and is written as a tensor product of independent functions, even before solving the Schrödinger equation. In more complex systems where there are electron-electron, electron-nucleus, nucleus-nucleus, and other interactions, the wave function should be written as a tensor product of entangled states after solving the Schrodinger equation. The aim of this study is to demonstrate to physics and chemistry teachers and students that there are different ways to view the quantum world. The many-worlds interpretation is simply another way of interpreting the solutions of the Schrodinger equation, rather than a new mathematical approach. The present work emphasizes the importance of understanding different interpretations of quantum mechanics and their implications for understanding the physical world. Keywords: Hydrogen atom spectrum, Schrodinger equation, Copenhagen school, Many-worlds interpretation.