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 Homework Statement:

A 3 dimensional box with volume size L^3, the inner potential is zero and the
potential in its bound is infinite. There is a particle with the mass m, if the
system's energy range between ##100E_0## until ##136E_0## with ##E_0=\frac{n^2\pi ^2}{2mL^2}##. Find all possible number of states by:
1. Direct method
2. Approximation using phi = 3.14
3. If particle filled with 15 particles and each states only could be filled with 1 particle and the system is in the lowest energy, find the system's energy!
 Relevant Equations:
 ##E_0=\frac{n^2\pi ^2}{2mL^2}##
I tried to find states in direct method using ##\frac{E}{E_0}=\:nx^2+ny^2+nz^2## and ##100\:<nx^2+ny^2+nz^2\:<\:136##
But it was too long, found it using phi approximation there are around 300 energy states, and Python find around 271 states using direct method but I need manual or recursive method to prove the direct method.
Python code: https://www.onlinepython.com/r4t0Fv7B3p
But it was too long, found it using phi approximation there are around 300 energy states, and Python find around 271 states using direct method but I need manual or recursive method to prove the direct method.
Python code: https://www.onlinepython.com/r4t0Fv7B3p
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