The relation from which discreteness in eigenvalue of the energy of bound state arises is $[x, p]=i\hbar$ followed by the rule that wavefunction should be normalizable. So my question is there a geometrical way to interpret this relation, may be in phase space, so that once I see some kind of commutator relation I can see what entity it is going to affect and how for example its discretization?

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    $\begingroup$ What you say is not quite true, the commutation relation is valid for free particles, but the energy spectrum of free particles is not discrete. You need some boundary conditions to induce discrete energy states. $\endgroup$ – Raskolnikov Mar 5 at 15:33

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