I.- [25 marks] The legendary Dr. Schrodinger has decided to hire you as his good Padawan. However, before finally signing the contract, he decides to put yourself to the test, for which he asks you to calculate numerically, using the derivative operator method seen in class, the first 25 energy eigenvalues ​​of the quantum system:

The good Dr. Schrodinger kindly shares with you the analytical solution of such a system:

Obtain your results using = 1, m = 1 and ~ = 1. Report the table of results obtained for the first 25 eigenvalues ​​of energy, as well as the percentage of relative error obtained with respect to the theoretical value. What is a major source of error in this problem, due to factor x2?

II.- [25 marks] By then, the legendary Dr. Schrodinger has already realized that he also has 23 other applications for his vacancy. Therefore, he also decides to challenge you to calculate numerically, using the shooting method (that’s right, Dr. Schrodinger wants to observe your research skills!), The first 25 eigenvalues ​​of energy of the following quantum system:

The good Dr. Schrodinger shares with you – again – and kindly the analytical solution to this quantum system:

Obtain your results using a = 1, m = 1 and ~ = 1. Report the table of results obtained, as well as the percentage of relative error obtained with respect to the theoretical value for the first 25 energy eigenvalues ​​of said system. Good luck with the hiring!

Deliverables: A printed document (and sent to my email) containing your results obtained, the MATLAB codes used (with their respective comments). Remember to include figures, bibliographic references, and conclusions as well as the corresponding flow diagram of the algorithm using in MATLAB.

DETAILED ASSIGNMENT

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