The measurement process

The measurement process - component in the wave functon. We...

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The measurement process Suppose I know my wave function at time is the sum of the two lowest-energy harmonic oscillator wave functions, (8.25) The introduction of the time independent wave function was through the separation . Together with the superposition for time-dependent wave functions, we find (8.26) The expectation value of , i.e., the expectation value of the energy is (8.27) The interpretation of probilities now gets more complicated. If we measure the energy, we don't expect an outcome , since there is no
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Unformatted text preview: component in the wave functon. We do expect or with 50 % propability, which leads to the right average. Actually simple mathematics shows that the result for the expectation value was just that, . We can generalise this result to stating that if (8.28) where are the eigenfunctions of an (Hermitean) operator , (8.29) then (8.30) and the probability that the outcome of a measurement of at time is is . Here we use orthogonality and completeness of the eigenfunctions of Hermitean operators....
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The measurement process - component in the wave functon. We...

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