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...field but retains many of the properties of the real numbers. [[Hermitian|Self-adjoint operator]]s on a [[Hilbert space]] (for example, self-adjoint square complex [[matri

...s. Each observable is represented by a densely defined [[Hermitian]] (or [[self-adjoint operator|self-adjoint]]) linear [[operator]] acting on the state space. Each eigenst

...least one (but usually more) irreducible representation. (Note that the [[self-adjoint operator|Hermiticity]] of ''V''_''k'' implies that its (''i,j'') element i

...ics]], energy, as any observable physical quantity, is represented by a [[self-adjoint operator]], usually designated by ''H'' in honor of [[William Rowan Hamilton]]. Most ...quantum mechanical energy operator (Hamilton operator) becomes finally the self-adjoint operator,