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- Title
Solving the one-dimensional time-independent Schrödinger equation with high accuracy: The LagrangeMesh Mathematica® package.
- Authors
del Valle, J. C.
- Abstract
In order to find the spectrum associated with the one-dimensional Schrödinger equation, we discuss the Lagrange Mesh Method (LMM) and its numerical implementation. After presenting a general overview of the theory behind the LMM, we introduce the LagrangeMesh package: the numerical implementation of the LMM in Mathematica ® . Using few lines of code, the package enables a quick home-computer and highly accurate computation of the spectrum and provides a practical tool to study a large class of systems in quantum mechanics. The main properties of the package are (i) the input is the potential function and the interval on which it is defined; and (ii) the accuracy in calculations and final results is controllable by the user. Due to its high accuracy and simple usage, the package may be used as a research and educational tool. As illustration, a highly accurate spectrum of some relevant quantum systems is obtained by employing the commands that the package offers.
- Subjects
NONRELATIVISTIC quantum mechanics; QUANTUM mechanics
- Publication
International Journal of Modern Physics C: Computational Physics & Physical Computation, 2024, Vol 35, Issue 1, p1
- ISSN
0129-1831
- Publication type
Article
- DOI
10.1142/S0129183124500116