• Support PF! Buy your school textbooks, materials and every day products Here!

Particle in a 3D box (Quantum)

  • Thread starter breeg
  • Start date
  • #1
1
0

Homework Statement



What are the degeneracies of the first four energy levels for a particle in a 3D box with a=b=1.5c?



Homework Equations



Exxnynz=h2/8m(nx2/a2+ny2/b2+nz2/c2)

For 1st level, the above = 3h2/8m
For 2nd level, the above = 6h2/8m
For 3rd level, the above = 9h2/8m
For 4th level, the above = 11h2/8m

The Attempt at a Solution



I think I finally grasped the basis of what the problem wants.

For the 1st level:

Exxnynz=(h2/(8m*1) + h2/(8m*1) + h2/8m*(1/1.5))*(1+1+(3/2))

So E1 1 3/2

3/2 was obtained because 1/1.5 is 2/3=c because a=b=1=1.5c so c=1/1.5=2/3

Is this correct? I'm just unsure about the rest of the energy levels. It seems like one can just pick numbers and force it to work so I'm lost on the proper degeneracy.
 

Answers and Replies

  • #2
BruceW
Homework Helper
3,611
119
For the 1st level:

Exxnynz=(h2/(8m*1) + h2/(8m*1) + h2/8m*(1/1.5))*(1+1+(3/2))
Why are you multiplying by (1+1+3/2)? I don't think you've got the idea. The quantum numbers each take on an integer value, and that is why the energy levels are different.
 

Related Threads on Particle in a 3D box (Quantum)

Replies
11
Views
3K
  • Last Post
Replies
12
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
8K
  • Last Post
Replies
8
Views
9K
  • Last Post
Replies
2
Views
828
Replies
1
Views
3K
  • Last Post
Replies
6
Views
4K
  • Last Post
Replies
2
Views
1K
Replies
6
Views
2K
Top