Solution Of The Time Dependent Schrodinger Equation Using The Higher Order Trotter-Suzuki Method

Dhea Chita Octavianty; Pekik Nurwantoro

doi:10.22146/jfi.v26i1.66637

Solution Of The Time Dependent Schrodinger Equation Using The Higher Order Trotter-Suzuki Method

https://doi.org/10.22146/jfi.v26i1.66637

Dhea Chita Octavianty^(1*), Pekik Nurwantoro⁽²⁾

(1) Universitas Gadjah Mada
(2) Universitas Gadjah Mada
(*) Corresponding Author

Abstract

We solve the solution of the Time-Dependent Schrodinger Equation (TDSE) using the higher-order Trotter-Suzuki Decomposition. We use The Gaussian function as a stationary state in a linear potential system. The TDSE solution using Baker - Campbell - Hausdorff was used to validate the results and to measure the accuracy of the Trotter - Suzuki decomposition. So that the difference between the Baker - Campbell - Hausdorff result and the Suzuki - Trotter decomposition is considered an error. The error of the TDSE solution by the Trotter - Suzuki second-order decomposition was lower than the first order. Meanwhile, the error of the TDSE solution by second-order hybrid will be lower than the second-order Trotter - Suzuki decomposition when the value of dx=0.1 and 0.05 with dt < 0.0001. The error comparison of these three methods is only valid when time t<1.

Keywords

Time-Dependend Schrodinger Equation, Trotter – Suzuki decomposition high order, Baker – Campbell – Hausdorff

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References

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DOI: https://doi.org/10.22146/jfi.v26i1.66637