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https://www.nist.gov/itl/math/acmd-seminar-volterra-integral-equation-approach-time-dependent-schrodinger-equation

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# ACMD Seminar: A Volterra Integral Equation Approach to the Time Dependent Schrödinger Equation

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Ryan Schneider*Department of Mathematics, UC San Diego*

Tuesday, May 24, 2022, 3:00-4:00 EDT (1:00-2:00 MDT)

**A video of this talk is available to NIST staff in the Math channel on NISTube, which is accessible from the NIST internal home page.**

**Abstract:**Numerical methods for solving differential equations are of particular importance for the time dependent Schrödinger equation (TDSE), for which analytic solutions typically do not exist. A common approach is to make a short time approximation, assuming that for a small enough time interval the Hamiltonian is more or less constant. While relatively simple to implement, short time approximations often require prohibitively small time steps to achieve high accuracy. To overcome this issue, we present an alternative approach that solves the TDSE by iterating a corresponding Volterra integral equation, handling the integrals involved with high order Gauss quadratures. In this talk, we explore established techniques for solving the TDSE, derive the new Volterra equation method, and show its application on a few numerical examples.

**Bio:**Ryan Schneider is a Ph.D. student in math at UC San Diego who has worked as an associate researcher at NIST for the last two year. Before that, he completed his undergraduate degree in math at Washington University in St. Louis. His research focuses on numerical methods and numerical linear algebra.

**Note:** This talk will be recorded to provide access to NIST staff and associates who could not be present to the time of the seminar. The recording will be made available in the Math channel on NISTube, which is accessible only on the NIST internal network. This recording could be released to the public through a Freedom of Information Act (FOIA) request. Do not discuss or visually present any sensitive (CUI/PII/BII) material. Ensure that no inappropriate material or any minors are contained within the background of any recording. (To facilitate this, we request that cameras of attendees are muted except when asking questions.)

**Host:** Barry Schneider

Mathematics and statistics

## Contacts

                -  Barry I. Schneider  barry.schneider@nist.gov      (301) 975-4685   
                -  Stephen Langer  stephen.langer@nist.gov      (301) 975-5423   
                -  Lochi Orr  lochi.orr@nist.gov      (410) 598-6986   

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