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Under what conditions does quantum mechanics reduce to classical mechanics?

  1. Oct 22, 2012 #1
    1. The problem statement, all variables and given/known data
    "At 310K thermal energy kT=4.28x(10^-21). Use the equation you derived above (which I worked out to be E=(n²h²)/(8mL²) )to determine under which conditions quantum mechanics reduces to classical mechanics."
    The hint was that "you need to find the value of mL² for which change in E between two adjacent energy levels is equal to kT".

    2. Relevant equations
    E=kt
    E=(n²h²)/(8mL²)

    3. The attempt at a solution
    I'm not quite sure how to start here, the only thing I've managed to do so far is:

    ((n2²-n1²)h²)/(8mL²)=4.28x(10^-21)

    I'm not sure what to do with so many unknowns, or what the question is actually asking me to calculate!
     
  2. jcsd
  3. Oct 22, 2012 #2
    Assuming the above is correct let n2 = 2 and let n1 = 1. Now solve for mL^2.

    Larger values of n2 will yield larger values of mL^2 which you should point out.
     
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