Traditional textbooks on quantum mechanics tend to introduce the mathematical formalism of the subject via Linear Algebra. However, this gives the wrong impression that all that is needed is to learn about complex matrices and that’s it! This is almost true but only if the systems being considered are modeled with finite-dimensional Hilbert spaces. As soon as you’re studying systems modeled with infinite-dimensional Hilbert spaces, then it’s no longer just Linear Algebra, instead you need
Linear Algebra Is Not Enough!
Linear Algebra Is Not Enough!
Linear Algebra Is Not Enough!
Traditional textbooks on quantum mechanics tend to introduce the mathematical formalism of the subject via Linear Algebra. However, this gives the wrong impression that all that is needed is to learn about complex matrices and that’s it! This is almost true but only if the systems being considered are modeled with finite-dimensional Hilbert spaces. As soon as you’re studying systems modeled with infinite-dimensional Hilbert spaces, then it’s no longer just Linear Algebra, instead you need