Physics 3333

Homework Set 2

Due Sept. 20, 1999

email to: phcox@tamuk.edu

Consider particles in harmonic oscillator potential wells. For a 1-dimensional simple harmonic oscillator,
 
 

Eground + nh bar omega,




where n is the quantum number, which can be 0,1,2,3…

For a particle in a 3-dimensional simple harmonic oscillator, or for 3 1-dimensional simple harmonic oscillators,
 
 

E= Eground + (n1 + n2 + n3) h har omega,




or grouping n1 + n2 + n3 = N,
 
 

E = Eground + Nh har omega.




A system consists of No oscillators, with an average energy (above Eground) per oscillator of between .99E0 and 1.01E0.

How many states are accessible if

    1. N0 = 1 and E0 = 5.0 h har omega (use no approximations)
    2. N0 = 1 and E0 = 5.5 h har omega (use no approximations)
    3. N0 = 3 and E0 = 5.0 h har omega (use no approximations)
    4. N0 = 3 and E0 = 5.5 h har omega (use no approximations)
    5. N0 = 100 and E0 = 5.5 h har omega