Can a measurement partially “collapse” a wavefunction?
Answers
Let's say I have a wavefunction ΨΨ which can be decomposed into a sum of it's energy eigenstates: Ψ=a|1⟩+b|3⟩+c|8⟩+d|10⟩ Ψ=a|1⟩+b|3⟩+c|8⟩+d|10⟩ Where, of course, |a|2+|b|2+|c|2+|d|2=1|a|2+|b|2+|c|2+|d|2=1. And let's say I have a device which can measure the energy of this wavefunction. Unfortunately, the device has an inherent uncertainty of ±3±3. I measure ΨΨ and find it to have an energy of 7±37±3. After my measurement the wavefunction has "collapsed" (to some extent?). I can think of a few possibilities for post-measurement ΨΨ: 1) ΨΨ really is in either |8⟩|8⟩ or |10⟩|10⟩. The problem statement is wrong: any uncertainly in energy measured is a laboratory issue. It must have an exact physical answer. 2) Ψ=c′|8⟩+d′|10⟩Ψ=c′|8⟩+d′|10⟩ Where, |c′|2+|d′|2=1|c′|2+|d′|2=1. I might even go so far as to say c′=c/(|c|2+|d|2)12c′=c/(|c|2+|d|2)12 My immediate answer: the measurement simply eliminated the possibility of the |1⟩|1⟩ and |3⟩|3⟩ eigenstates. 3) Ψ=e|4⟩+f|5⟩+g|6⟩+h|7⟩+k|8⟩+m|9⟩+n|10⟩Ψ=e|4⟩+f|5⟩+g|6⟩+h|7⟩+k|8⟩+m|9⟩+n|10⟩ The "measurement" isn't really a measurement; just a disruption to the wavefunction.
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Can a measurement partially “collapse” a wavefunction?
Collapse in wave function
♣ Many theory cannot prove it.
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