[2025.1.8] 11:00-12:00 ❘ Dr. Yair Mulian (AS) : On a unitary solution for the Schrödinger equation
******** Special Seminar ********
Speaker ：Dr. Yair Mulian (AS)
Title ： On a unitary solution for the Schrödinger equation
Time ：11:00-12:00, Wednesday, 2025/1/8
Place ：P512, 5F, General Building III, Nat'l Tsing Hua Univ.
Host ： Prof. Ray-Kuang Lee (NTHU)
Abstract:
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 the case of a singular Hamiltonian and provide a new methodology that is not based on the assumption that the underlying space is L^2(R). 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.
Speaker ：Dr. Yair Mulian (AS)
Title ： On a unitary solution for the Schrödinger equation
Time ：11:00-12:00, Wednesday, 2025/1/8
Place ：P512, 5F, General Building III, Nat'l Tsing Hua Univ.
Host ： Prof. Ray-Kuang Lee (NTHU)
Abstract:
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 the case of a singular Hamiltonian and provide a new methodology that is not based on the assumption that the underlying space is L^2(R). 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.