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# Lect09 - Labs will be in room 257(2nd floor this week Need...

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Labs will be in room 257 (2 nd floor) this week. Need AD sign-on. See supplementary notes at end of this lecture to try to get big picture for QM See website for link to new formula sheet, through this week. http://www.falstad.com/qm1d/

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Superposition & Time-Dependent Quantum States (x,t) | 2 U= x U= 0 x L
Overview Overview z Superposition of states and particle motion z ‘Packet States’ in a Box z Measurement in quantum physics z Schrödinger’s Cat z Time-Energy Uncertainty Principle

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Time Time - - independent independent SEQ SEQ z Up to now, we have considered quantum particles in stationary states ,” and have ignored their time dependence Remember that these special states were associated with a single energy (from solution to the SEQ) “eigenstates” of energy ) ( ) ( ) ( ) ( 2 2 2 2 x E x x U dx x d m ψ ψ ψ = + = U= ψ (x) 0 L U= n=1 n=2 x n=3 “Functions that fit”: ( λ = 2L/n) ψ (x) 0 L x “Doesn’t fit”:
Superposition: a roadmap Superposition: a roadmap z The fundamental (time-dependent) SEQ is LINEAR so its solutions obey superposition. z There is NO RULE forbidding states with a range of different E, just as there was no rule forbidding states with ranges of x or p. z E.g. Superpositions of the n=1 and n=2 states of particle in box z The states of fixed E did nothing! They just sat there. http://www.falstad.com/qm1d/ z (actually just rotated in complex plane- no change in probability density) z All interesting events come from states with more than one E, superpositions of the single-E states we described. z So now we have to learn how to treat those mathematically. (x,t) | 2 U= U= 0 x L

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