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In quantum mechanics, what`s the definition of the "two-level systems"? I understand that the state vector is in the form |Ψ>=a|1>+b|2>, where |1>,|2> is a basis of the state space.

Then i think of the particle in a box. The energy is quantized (lets say that the possible values are E1 and E2) while position x is continuous. So, in the first case we would have: |Ψ>=a|E1>+b|E2> and in the second one: |Ψ>=Integral(Ψ(x) |x> dx).

So if we use as a basis the eigenstates of the energy, our system would be a "two-level system". However, in {x} representation, we would have an "infinite-level system".

So what`s the definition of a "two-level system" since the number of levels depend on the basis we use?

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# Homework Help: Two-Level Systems

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