Uncertainty Principle Question

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SUMMARY

The discussion revolves around estimating the uncertainty in the momentum and wavelength of a photon emitted from a laser pulse measuring 30 microns wide. Using the uncertainty principle ΔxΔp ≥ h/4π and the momentum formula p = h/λ, the user calculated the uncertainty in momentum (Δp) to be 1.757 × 10-30 kg·m/s. Subsequently, they derived the uncertainty in wavelength (Δλ) to be 0.000377 m, assuming a nominal wavelength of 800 nm. The methodology applied in both parts of the problem is correct and aligns with quantum mechanics principles.

PREREQUISITES
  • Understanding of the Heisenberg Uncertainty Principle
  • Familiarity with Planck's constant (h = 6.626 × 10-34 J·s)
  • Knowledge of photon momentum formula (p = h/λ)
  • Basic concepts of light wavelength and its measurement
NEXT STEPS
  • Study the implications of the Heisenberg Uncertainty Principle in quantum mechanics
  • Explore advanced applications of photon momentum in laser technology
  • Learn about the relationship between wavelength and energy in photons
  • Investigate experimental methods for measuring photon properties
USEFUL FOR

Students and professionals in physics, particularly those focusing on quantum mechanics, optics, and laser technology. This discussion is beneficial for anyone seeking to deepen their understanding of photon behavior and uncertainty principles.

lee_sarah76
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Homework Statement



Laser can now be designed to emit pulses of light smaller than 30 microns wide
in their direction of motion.

(a) Estimate the uncertainty in the momentum of a
photon in such a pulse.

(b) The momentum of a photon is p=h/λ. Estimate the
uncertainty in the wavelength of a photon in the pulse, assuming a nominal
wavelength of 800 nm.


Homework Equations



ΔxΔp ≥ h/4π, p = h/λ

h being Planck's constant of 6.626 * 10-34 J*s

The Attempt at a Solution



My confusion with this problem stems from the fact that I'm not sure if Δx = 30*10-6m

If that is the case, then I did Δp ≥ h/4π*Δx.

Part a: Δp ≥ 1.757 * 10-30 kg*m/s

For part b, I then took the Δp value of 1.757 * 10-30 kg*m/s and plugged it into p = h/λ. I then got λ = 0.000377 m.

Is this the right method?
 
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Seems good.
 

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