Parpcle Duality, Probability and Uncertainty-‐ Principle

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Parpcle Duality, Probability and Uncertainty-‐ Principle

Ch 38. Wave-Par.cle Duality, Probability and Uncertainty- Principle Ph274 – Modern Physics 2/29/2016 Prof. Pui Lam Learning Outcomes (1) Understand the “Principle of Complementarity” (2) Understand how wave interference paern can be interpreted as probability of a photon landing on the screen. (3) Understand the “Uncertainty Principle” Principle of Complementarity • “The wave descrip.ons and the par.cle descrip.ons are complementary. That is, we need both to complete our model of nature, but will never need to use both at the same .me to describe a single part of an occurrence.” • Note: Although we never need to use both at the same .me to describe a single part of an occurrence, some results can be explained by either the wave or par.cle descrip.on, see next slide for an example. Diffrac.on at very low intensity – introduce the concept of probabilis.c mo.on • Consider performing a single slit diffrac.on with light intensity so low that prac.cally only one photon going through the slit at a .me. • According to quantum theory, aer the photon exit the slit, its momentum is uncertain (Uncertainty Principle). The photon can exit at any angle with some probability. • If we collect the photons over a period .me, the resul.ng probabilis.c paern resembles the diffrac.on paern from wave theory. • BoRom line: At the quantum scale, mo.ons are probabilis.c. Quantum theory provides a method to calculate the probability. Figure 38.16 Uncertainty Principle • Use single slit diffrac.on as an example: • Slit width =a, that means the locaon of the photon in the “y-direc.on” can be anywhere within a=> the y-posi.on has an uncertain, Δy=a. • We will use the width of the central maximum to es.mate the uncertainty of the y-momentum. • Δpy/px=tanθ~sinθ~λ/a; note: px=h/λ • =>Δy Δpy~h The more precise statement of the Uncertainty Principle h is: y p ! ; Δ Δ y ≥ 2 ! ≡ 2π Figure 38.17 Other Uncertain Relaonships x p ! Δ Δ x ≥ 2 y p ! Δ Δ y ≥ 2 z p ! Δ Δ z ≥ 2 ΔtΔE ≥ ! 2 Figure 38.19 .

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