Gamma ray microscope method | Quantum mechanics | Physical basis of quantum mechanics

Proof of uncertainty principle

Gamma ray microscope method (Thought experiment)

• Let electron whose position (x) and momentum (p) is to be determined is initially at P
• From diffraction theory, the limit of resolution of microscope

            Δx = λ / 2 sin θ

• Δx = Distance between two points upto which they can be seen separately.
• Δx = Maximum uncertainty in position of electron
• Since the wavelength of 𝛾-ray is small, so we choose it because it decreases Δx
• Let at least one 𝛾-ray photon be scattered by the electron into the microscope so that the electron is visible.
• In this process the frequency and wavelength of the scattered photon is changed and the electron suffers a Compton recoil by gaining the momentum.
• If λ = wavelength of the scattered photon, then the momentum of the scattered photon, p = h / λ
• Since the scattered photon can be scattered in any direction from PA to PB, so the x-component of momentum will be from [(h / λ) sin (-θ)] to (h / λ) sin θ] i.e., from - [(h / λ) sin θ] to (h / λ) sin θ
• If λ՛ = wavelength of incident photon, then momentum of incident photon, p՛ = h / λ՛
• Therefore change in momentum of photon will lie between

• Thus microscope is obeying the Heisenberg’s uncertainty principle during the measurement of position and momentum of the particle simultaneously.
• To know more about Gamma ray microscope method as a proof of uncertainty principle in English please click on the link https://youtu.be/Mm3BqM1ZlWs and bilingual (Hindi/English) https://youtu.be/R0Z2k3vKL5Q