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lecture8 - 5.61 F all 2007 Lecture #8 page 1 QUANTUM...

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5.61 Fall 2007 Lecture #8 page 1 QUANTUM MECHANICAL PARTICLE IN A BOX Summary so far: V ( x < 0, x > a ) = ψ ( x < 0, x > a ) = 0 V ( 0 x a ) = 0 ( 0 x a ) = B sin n π a x n V ( x ) 0 n 2 h 2 n 2 a a E n = 8 ma 2 k = a λ = n n = 1,2,3,. .. 0 x What is the “wavefunction” x ( ) ? Max Born interpretation: ( ) 2 x x is a probability distribution or probability density for the particle x = * ( ) ( ) x dx is the probability of finding the particle in the interval ( ) 2 between and + dx This is a profound change in the way we view nature!! We can only know the probability of the result of a measurement – we can’t always know it with certainty! Makes us re-think what is “deterministic” in nature. Easy implication: Normalization of the wavefunction x 2 x dx = probability of finding particle in interval ( ) 2 x 1 The total probability of finding the particle somewhere must be 1. For a single particle in a box,
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5.61 Fall 2007 Lecture #8 page 2 a ( ) 2 0 ψ ( ) 2 Normalization condition −∞ x dx = x dx = 1 a n π x
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This note was uploaded on 09/24/2011 for the course MATH 1090 taught by Professor Greenwood during the Spring '08 term at MIT.

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lecture8 - 5.61 F all 2007 Lecture #8 page 1 QUANTUM...

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