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Derive the approximate form of Heisenberg’s uncertainty
Chapter 29, Problem 71(choose chapter or problem)
Problem 71PE
Derive the approximate form of Heisenberg’s uncertainty principle for energy and time, ΔEΔt ≈ h , using the following arguments: Since the position of a particle is uncertain by Δx ≈ λ , where λ is the wavelength of the photon used to examine it, there is an uncertainty in the time the photon takes to traverse Δx . Furthermore, the photon has an energy related to its wavelength, and it can transfer some or all of this energy to the object being examined. Thus the uncertainty in the energy of the object is also related to λ . Find Δt and ΔE ; then multiply them to give the approximate uncertainty principle.
Questions & Answers
QUESTION:
Problem 71PE
Derive the approximate form of Heisenberg’s uncertainty principle for energy and time, ΔEΔt ≈ h , using the following arguments: Since the position of a particle is uncertain by Δx ≈ λ , where λ is the wavelength of the photon used to examine it, there is an uncertainty in the time the photon takes to traverse Δx . Furthermore, the photon has an energy related to its wavelength, and it can transfer some or all of this energy to the object being examined. Thus the uncertainty in the energy of the object is also related to λ . Find Δt and ΔE ; then multiply them to give the approximate uncertainty principle.
ANSWER:
Solution 71PE