Under what conditions does quantum mechanics reduce to classical mechanics?

[amberbarton]

Homework Statement

"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".

Homework Equations

E=kt
E=(n²h²)/(8mL²)

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!

 

[Spinnor]

...


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!

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.