Quantum mechanics is ultimately and fundamentally a framework for understanding Nature through the formalism of linear algebra, vector spaces, and the like. In principle, your study of linear algebra from an introductory mathematics course would be necessary and sufficient background for studying quantum mechanics, but such a course is typically firmly rooted in the study of matrices and their properties. This is definitely relevant for quantum mechanics, but we will need a more general approach to linear algebra to be able to describe the dynamics of interesting physical systems and make predictions. Perhaps the most familiar and important linear operator, the derivative, was not even discussed within that context in a course on linear algebra. Because of this familiarity, studying properties of the derivative is an excellent place to begin to dip our toes into the shallow waters of the formalism of quantum mechanics.
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