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lec24 - ∂ 2 ψ ∂ x 2 8 π 2 m h 2 E − U x = ©2008 by...

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11/27/11 1 Classical View of Waves & Particles
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11/27/11 2 Quantum View 1924 Louis de Broglie: ...think of an electron or any other particle as a matter wave that transfers energy and momentum to other matter at points ..... de Broglie wavelength of a moving particle: λ = h p ©2008 by W.H. Freeman and Company
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Example: 11/27/11 3 Electrons in an electron beam have a de Broglie wavelength of 242 picometers. What is the kinetic energy in eV? h= 6.63 x 10 -34 Js m=9.1x10 -31 kg
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Double-slit Interference 11/27/11 4
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©2008 by W.H. Freeman and Company Quantum View
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11/27/11 6 Quantum View In quantum regime: *all objects, including light & electrons, can exhibit interference *all objects, including light & electrons, carry energy in discrete amounts. These discrete “parcels” are called quanta.
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11/27/11 7 Example 28.5 from textbook
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11/27/11 8 Wave Function ...motion of a particle wave is described by a wave function ..... Schrodinger Equation for 1D motion:
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Unformatted text preview: ∂ 2 ψ ∂ x 2 + 8 π 2 m h 2 E − U ( x ) [ ] = ©2008 by W.H. Freeman and Company 11/27/11 9 Wave Function 11/27/11 10 Heisenberg Uncertainty Principle Minimum uncertainty: Heisenberg Uncertainty Principle: 11/27/11 11 Example Δ x Δ p = h 2 π Key Idea: Assume that an electron is moving along an x axis and that you measure its speed to be 2.05x10-6 m/s, which can be known with a precision of 0.50%. What is the minimum uncertainty with which you can simultaneously measure the position of the electron along the x axis? 100 atomic diameters. given electron’s speed, no need to pin down an electron’s position to any greater precision. 11/27/11 12 Tunneling ©2008 by W.H. Freeman and Company Tunneling at an Optical Beam-splitter 11/27/11 14 Tunneling electrons ©2008 by W.H. Freeman and Company ©2008 by W.H. Freeman and Company 11/27/11 17 Electromagnetic Spectrum...
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