lecture_13

# lecture_13 - 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 CHAPTER 5 Wave Properties of Matter and Quantum Mechanics I Wave Properties of Matter and Quantum Mechanics I I thus arrived at the overall concept which guided my studies: for both matter and radiations, light in particular, it is necessary to introduce the corpuscle concept and the wave concept at the same time. - Louis de Broglie, 1929

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Classical Waves: A Review A wave is a propagating disturbance in a deformable, elastic medium. Medium: air (sound waves) water (water waves) Vacuum (EM waves) (E-B fields: an EM wave is its own medium) All waves transport energy; some transport momentum, and some even angular momentum. At any given instant, the state of a wave is completely specified by its amplitude throughout space, and by the time derivative of this amplitude. The simplest kind of a wave is a harmonic wave , Ψ ( x , t ) = A cos( kx t + φ ) λ= 2 π k f = ϖ 2
The velocity of the wave crest or the wave trough of a harmonic wave is called the phase velocity: At crest ( kx t + φ ) = 0 kdx dt = 0 v p = dx dt = ϖ k f If v p depends on k , or λ , the medium in which the wave propagates is said to be dispersive . e . g . water waves in deep water = gk v p = g λ 2 π

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Principle of Superposition When two or more waves arrive at any given point, the resultant instantaneous amplitude is the sum of the individual instantaneous amplitudes.
Depending on SIGN: Constructive Interference Destructive Interference Example : Two harmonic waves of equal amplitudes are simultaneously propagating along the x-axis in opposite directions. What is the net wave? Ψ 1 = A sin( kx t ) Ψ 2 = A sin( kx + ϖ t ) Ψ=Ψ 1 + Ψ 2 = A sin( kx t ) + sin( kx + ϖ t ) [ ] Trigonometric identity : sin α+ sin β= 2sin 1 2 ( α+β )cos 1 2 ( α-β ) Ψ= 2 A sin kx cos ϖ t STANDING WAVE

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String with both ends FIXED Ψ= 2 A sin kx cos ϖ t kL = n π 2 λ L = n n = 2 L n
Diffraction Diffraction is the bending of a wave around an obstacle in its path. The amount of diffraction depends on the relative size of the

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## This note was uploaded on 04/15/2008 for the course PHY 361 taught by Professor Alarcon during the Spring '08 term at ASU.

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lecture_13 - CHAPTER 5 Wave Properties of Matter and...

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