Accessible States for Boson Particles

Bosons: Particles with integer spin (s = 0, 1, 2, etc.).

Main Question: How can we place N boson particle with total amount of energy β in γ energy level with degeneracy g_i = α ?

Solution: We should calculate statistical weights with average particle number in each energy state.

Bosons are particles that follows **Bose-Einstein Statistics.

We can calculate statistical weight of the system by following fuction according to Bose-Einstein Statistics.

g_i -> degeneracy number of energy states

N_i -> number of particles occupies certain energy levels

$http://latex.codecogs.com/svg.latex?\Omega_k(BE) = \prod_i \frac{(g_i + N_i-1)!}{N_i! (g_i -1)}$

And the sum of the microscopic states will be

$http://latex.codecogs.com/svg.latex?\Omega(BE) = \sum_k \Omega_k (BE)$

Average number of particles in every energy level calculated by

$http://latex.codecogs.com/svg.latex?\overline{n(BE)} = \frac{1}{\Omega(BE)}\sum_k n_k \Omega_k$

And we can also compare this system with Maxwell-Boltzmann Statistics. Bosons follow or not?

We can calculate statistical weight of the system by following fuction according to Maxwell-Boltzmann Statistics.

$\Omega_k(MB) = N! \prod_i \frac{g_i^{N_i}}{N_i!}$

We need to generate particle distribution table. In order to calculate how many bosons occupy whics energy level, I have used some basic mathematical tricks.

1) Total number of particles in a row must be equal to total number of particles that we have entered.

2) $http://latex.codecogs.com/svg.latex?\sum_{i=1}^{N} a_n(n-1) =\sum_{i=1}^{N} a_n = E_{Total}$ , $a_n \in \mathbb{N}$ where $a_n$ is the number of particles can occupy an energy level.

Licence

Released under licence: the GPL version 3 license.

Using without reference is, among other things, against the current license agreement (GPL).

Scientific or technical publications resulting from projects using this code are required to citate.

Usage

You can enter defined total number of particles and proper amount of energy and degeneracy number.

Defined Total Number of Particles: 3,4,5,6,7,8,9,10

Total Number of Particles:

Total Amount of Energy:

Degeneracy number: