# Quantum Model

For two distinguishable, non-interacting particles in a box, Quantum Mechanics says the energy must be, for each individual particle,

E = (h^2)/(8mL^2)*[(n_x)^2 + (n_y)^2 + (n_z)^2)

where L is the length of one side of the cube, m is the mass of the particle, and the n's are independent integers that can take any value from 1 and up,

n_x = 1,2,3,4,K

n_y = 1,2,3,4,K

n_z = 1,2,3,4,K

In other words, the individual n's determine the microstates.

If the total energy is E = (h^2)/(8mL^2)(12) what is the multiplicity of that state?

Â© BrainMass Inc. brainmass.com February 24, 2021, 2:24 pm ad1c9bdddfhttps://brainmass.com/physics/energy/quantum-model-non-interacting-particles-box-18483

#### Solution Preview

Hi,

First, you have to realize that because the two particles are symmetrical, there are a lot of equivalent states ie. for particle 1, P1(nx, ny, nz) we can have P1(1, 2, 1) and it will be equal to P1(2, 1, ...

#### Solution Summary

The expert examines quantum models of non-interacting particles in a box. We have to solve P1(nx, ny, nz) + P2(nx, ny, nz) = 12.