Lecture_05

Lecture_05 - PHYS 342 Fall 2010 Lecture 05: de Broglie...

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PHYS 342 Fall 2010 Lecture 05: de Broglie “Matter Waves”, and the 1D Schrödinger Wave Equation Lecture 05 Ron Reifenberger Birck Nanotechnology Center Purdue University
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d >> λ LIGHT PARTICLE m d Dual Character d >> λ deBroglie rmat’s Principle Ray Nature Wave Nature Particle Nature d m Wave Nature d ~ λ d ~ λ deBroglie box d d Fer
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Notation so far…. 34 2 6.626 10 2 ( ) c f h E h f f h J s E p EM wave c λ π ϖ - = = = = = × = ( ) ( ) 2 2 deBroglie deBroglie hf h p photon c h particle p h p k π λ = = = = =
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So if particles behave like waves, what is the equation that describes the motion of these “matter-waves”? A Fundamental Question How does the wavelength of a matter-wave change with position and time?
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Schrödinger Wave Equation (1926) Can’t be derived, just like Newton’s F=ma can’t be derived Schrödinger’s equation is justified by agreement with experiment Solves a large number of non-relativistic problems in atomic physics Must be modified to include relativistic effects Describes the behavior of the wave field of a particle, the so- called matter wave
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(Hamilton-Jacobi; 1834) E hf ϖ = = Planck (1901), Einstein (1905), Bohr (1911) : 2 h h π = = 2 2 p KE PE E U m = + = + e Broglie (1923) Wave-like properties of matter Describes how an object interacts with its environment Where to Start? 2 k p λ π λ = de Broglie (1923) : k is called the wavevector. Anytime you see k U , think F=-dU/dx
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Lecture_05 - PHYS 342 Fall 2010 Lecture 05: de Broglie...

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