Formula relating to Uncertainty Principle

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SUMMARY

The discussion centers on the derivation of the formula relating to the Uncertainty Principle, specifically transitioning from Δt ~ (h-bar)/(hc/λ) to Δt ~ λ/2∏c. The key equations involved are ΔE = hc/λ and ΔEΔt ~ (h-bar)/E. The simplification process is clarified by noting that h-bar equals h/(2π), which facilitates the conversion between the two expressions. This highlights the importance of understanding the relationships between Planck's constant and the speed of light in quantum mechanics.

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  • Understanding of quantum mechanics principles
  • Familiarity with Planck's constant and its notation
  • Knowledge of basic algebraic manipulation of equations
  • Concept of the Uncertainty Principle in physics
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  • Study the derivation of the Uncertainty Principle in quantum mechanics
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Students of physics, particularly those studying quantum mechanics, educators teaching the Uncertainty Principle, and anyone interested in the mathematical foundations of quantum theories.

ZedCar
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Homework Statement



I was looking at a solution inmy notes which begins:

ΔE = hc/λ -1st eqn

ΔEΔt ~ (h-bar)/E -2nd eqn
Δt ~ (h-bar)/ (hc/λ)
Δt ~ λ/2∏c

(where 'c' is the speed of light)

What formula has been used to go from:

Δt ~ (h-bar)/ (hc/λ)
to
Δt ~ λ/2∏c

Homework Equations





The Attempt at a Solution

 
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It's just simplifying. To divide by a fraction, flip the fraction over and multiply. h-bar = h/(2pi).
 
Cheers for that TSny...!
 

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