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particular to the notion of density matrices, which we explore. see how the axioms of quantum mechanics describe in a very simple and nice. The operator algebra is basis independent. Even if the matrices in Eq. (18) do not look like coordinate and momentum in any intuitive way, but their commutationThis elementary text introduces basic quantum mechanics to undergraduates with no background in mathematics beyond algebra. Containing more than 100 This elementary text introduces basic quantum mechanics to undergraduates with no background in mathematics beyond algebra. Containing more than 100 The reference for this material is Kinzel and Reents, p. 47-51. We first discuss the exactly solvable case of the simple harmonic oscillator. The Hamiltonian is This elementary text introduces basic quantum mechanics to undergraduates with no background in mathematics beyond algebra. Containing more than 100