Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Uncertainty Principle textbook equation

  1. Aug 23, 2013 #1
    I have been going through my Physics text book to brush up on my Quantum Mechanics before starting my next QM course next academic year and the Heisenberg uncertainty principle for position and momentum is written as ΔxΔp ≥ h-bar when I thought it was ΔxΔp ≥ (h-bar)/2. Other sources say it is the latter so am I missing something? Or is the text book just wrong?
     
  2. jcsd
  3. Aug 23, 2013 #2
    The latter (hbar/2), assuming that Δx and Δp are interpreted as standard deviations from their respective means.
     
  4. Aug 23, 2013 #3
    So are there circumstances when ΔxΔp ≥ h-bar is correct? Say when you are not dealing with standard deviations?
     
  5. Aug 23, 2013 #4

    jtbell

    User Avatar

    Staff: Mentor

    When you're interested mainly in order-of-magnitude estimates (powers of ten), a factor of 2 or 1/2 or something like that doesn't affect the result significantly.
     
  6. Aug 23, 2013 #5

    vanhees71

    User Avatar
    Science Advisor
    2016 Award

    The correct Heisenberg-Robertson uncertainty relation is
    [tex]\Delta x \Delta p \geq \frac{\hbar}{2}.[/tex]
    You can show that the Gaussian wave packets are the only ones, where the equality sign is valid.
     
  7. Aug 27, 2013 #6
    OK, thanks for clearing that up.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Uncertainty Principle textbook equation
Loading...