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I don't know much about QM. I'm reading lecture notes at the moment. Angular momentum is discussed. The ladder operators for the angular-momentum z-component are defined, it is shown that <L_z>^2 <= <L^2>, so the z component of angular momentum is bounded by the absolute value of angular momentum. And then, I don't know why, it is stated that "evidently" the angular momentum eigenvalues are discrete. Why is that so? I see somehow that this is the case when I solve the Schrödinger equation in spherical coordinates by seperation. But this did not happen in the text yet. Can this be seen purely algebraically? Is it true, maybe, that the eigenvalue spectrum is discrete if it is bounded?

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# Does the existence of a ladder operator imply that the eigenvalues are discrete?

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