Ch 38. Wave-Parcle 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 descripons and the parcle descripons 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 parcle descripon, see next slide for an example. Diffracon at very low intensity – introduce the concept of probabilisc moon • Consider performing a single slit diffracon with light intensity so low that praccally 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 resulng probabilisc paern resembles the diffracon paern from wave theory. • Boom line: At the quantum scale, moons are probabilisc. Quantum theory provides a method to calculate the probability. Figure 38.16 Uncertainty Principle

• Use single slit diffracon as an example: • Slit width =a, that means the locaon of the photon in the “y-direcon” can be anywhere within a=> the y-posion has an uncertain, Δy=a. • We will use the width of the central maximum to esmate 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