- #1
HAMJOOP
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Question
Particle in a box (2D)
Determine the energy levels (degeneracy) of the lowest three
I found that E = A (4a^2 + b^2)
where A is a constant
a and b are positive integers (principle quantum number)
My steps
I assume 4a^2 + b^2 = k
where k is also a positive integer
The minimum value of a and b are 1, so k ≥ 5
I would like to find the combination of a and b for a given k.
But I don't know how to solve integral solution.
Is there any systematic methods apart from trial and error ?
Particle in a box (2D)
Determine the energy levels (degeneracy) of the lowest three
I found that E = A (4a^2 + b^2)
where A is a constant
a and b are positive integers (principle quantum number)
My steps
I assume 4a^2 + b^2 = k
where k is also a positive integer
The minimum value of a and b are 1, so k ≥ 5
I would like to find the combination of a and b for a given k.
But I don't know how to solve integral solution.
Is there any systematic methods apart from trial and error ?