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 energyto 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.
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 energyto 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.
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter28: Quantum Physics
Section: Chapter Questions
Problem 3OQ
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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.
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