The probability to get a particular measured result depends on the probability amplitude, given by the inner product of the physical state | ψ ψ ⟩ ⟩ with the basis vectors { | ϕ ϕ i ⟩ ⟩ } that diagonalize the measurement operator. For a physical state that is measured after it has evolved in time, the probability amplitude can be described either by the inner product of the physical state after time evolution with the relevant basis vectors, or equivalently by the inner product of the physical state with the basis vectors that are evolved backwards in time. Using the time evolution operator e − − i H ^ ^ t / ℏ ℏ , we have: