Manfra16-2011

Manfra16-2011 - CHAPTER 5 Wave Properties of Matter and...

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5.1 X-Ray Scattering 5.2 De Broglie Waves 5.3 Electron Scattering 5.4 Wave Motion 5.5 Waves or Particles? 5.6 Uncertainty Principle 5.7 Probability, Wave Functions, and the Copenhagen Interpretation 5.8 Particle in a Box Wave Properties of Matter and Quantum Mechanics I Problems due next Monday: March 7th, Chapter 5: 7, 22, 25, 27, 28, 36, 37, 44, 48, 54 Louis de Broglie (1892-1987) CHAPTER 5

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Since we’re always uncertain as to the exact position, , of a particle, for example, an electron somewhere inside an atom, the particle can’t have zero kinetic energy: Kinetic Energy Minimum p x ∆ ≥ = h h l so: x ∆ = l The average of a positive quantity must always equal or exceed its uncertainty: ave p p x ≥ ∆ ≥ = h h l 2 2 2 ( ) 2 2 2 ave ave p p K m m m = h l
Okay, if particles are also waves, what’s waving? Probability The wave function determines the likelihood (or probability) of finding a particle at a particular position in space at a given time: 5.7: Probability, Wave Functions, and the Copenhagen Interpretation The total probability of finding the particle is 1. Forcing this condition on the wave function is called normalization. 2 ) ( ) ( x x P Ψ = 2 1 2 ( ) x x x dx Ψ 2 ( ) 1 x dx -∞ Ψ = The probability of the particle being between x 1 and x 2 is given by:

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A particle (wave) of mass m is in a one-dimensional box of width . The box puts boundary conditions on the wave. The wave function must be zero at the walls of the box and on the outside. In order for the probability to vanish at the walls, we
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This note was uploaded on 04/23/2011 for the course PHYS 342 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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Manfra16-2011 - CHAPTER 5 Wave Properties of Matter and...

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