Title: Solving the Time Dependent Schrödinger Equation Using Volterra Integral Equations
Researchers at NIST have developed a new method for solving the time dependent Schrödinger equation (TDSE), a fundamental equation in quantum mechanics. The TDSE describes how the quantum state of a physical system changes over time, but finding solutions is challenging because analytic solutions rarely exist.
The new approach involves converting the TDSE into a Volterra integral equation, which can be solved using numerical methods. This allows the equation to be handled more effectively than traditional short time approximations, which often require very small time steps to maintain accuracy.
The method was presented by Ryan Schneider, a Ph.D. student in mathematics at UC San Diego and associate researcher at NIST. Schneider’s research focuses on numerical methods and linear algebra. The talk was recorded and is available to NIST staff internally, with the possibility of public release through a Freedom of Information Act request.
Keywords: Differential Equations, Volterra Integral Equation, Gauss Quadratures
