In order to find the spectrum associated with the one-dimensional
Schr\"oodinger equation, we discuss the Lagrange Mesh method (LMM) and its
numerical implementation for bound states. 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 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 basically
the potential function and the interval on which is defined; and (ii) the
accuracy in calculations and final results is controllable by the user. As
illustration, a highly accurate spectrum of some relevant quantum systems is
obtained by employing the commands that the package offers. In fact, the
present work can be regarded as a user guide based on worked examples.Comment: File LagrangeMesh.wl can be provided to the interested reader, just
contact the author via email. Alternatively, it can be found at
https://github.com/JuanCarlosdelValle/LagrangeMesh-Packag