On a unitary solution for the Schrödinger equation

Yair Mulian^1*

¹Physics, Academia Sinica, Taipei, Taiwan

* Presenter:Yair Mulian, email:yair25m@gmail.com

For almost 75 years, the general solution for the Schrödinger equation was assumed to be generated by an exponential or a time-ordered exponential known as the Dyson series. We study the unitarity of this solution in case of singular Hamiltonian and provide a new methodology that is not based on the assumption that the underlying space is L^2. Then, an alternative operator for generating the time evolution is suggested that is manifestly unitary, regardless of the choice of the Hamiltonian. The new construction involves an additional positive operator that normalizes the wave-function locally and allows us to preserve unitary even on infinite dimensional spaces. Our considerations show that Schrödinger's and Liouville's equations are, in fact, two sides of the same coin, and together they become the unified description of quantum systems. Based on arxiv.org/abs/2402.18499 which recently has been accepted for publication.

Keywords: Schrödinger equation, Unitarity, Quantum mechanics, Time evolution, Entanglement