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Lect16

# Lect16 - PHYS 172 Modern Mechanics Lecture 16 Multiparticle...

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Fall 2011 PHYS 172: Modern Mechanics Lecture 16 – Multiparticle Systems Read 9.1 – 9.4 1

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Quantizing two interacting atoms E = 1 2 mv 2 + 1 2 kx 2 = 1 2 kA max 2 Any value of A is allowed any E is possible. Classical harmonic oscillator: Quantum harmonic oscillator: U = k s s 2 1 0 0 E E ! = + ! 2 0 0 2 E E ! = + ! U = k s s 2 Energy levels: 1 0 0 2 N E N ! ! = + ! ! 0 / s k m ! = 34 1.05 10 J s 2 h ! " # = \$ % ! 0 s k m ! = ! ! 1 0 0 2 E ! = ! equidistant spacing ground state 2
Time to Throw Things BALL We need to understand Center of Mass BATON 3

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The Center of Mass where This is a weighted average of the positions -- each position appears in proportion to its mass 4
1 r ! 3 r ! 2 r ! cm r ! 1 1 2 2 3 3 1 2 3 cm m r m r m r r m m m + + + ! + + + ! ! ! " ! " The Center of Mass 5

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Motion of the Center of Mass 1) Take one time derivative: Same as: (Good!) 6
Motion of the Center of Mass 1) Take a second time derivative: This says that the motion of the center of mass looks just like what would happen if all forces were applied to the total mass, as a point particle located at the center of mass position!

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