1) For two distinguishable, non-interacting particles in a ...
1) For two distinguishable, non-interacting particles in a box, Quantum Mechanics says the energy must be, for each individual particle,
[pic]
[pic] 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, [pic]
In other words, the individual n’s determine the microstates.
For two non-interacting particles, the Etot is the sum of each of the individual particles energies. Suppose that the particles each have the same mass.
If the total energy is [pic], what is the multiplicity of that state? (5 points)
For example, when [pic] we can find the multiplicity by making a chart:
|Energy | |n values |multiplicity |
| |Particle 1’s state |Particle 2’s state | |
|[pic] |nx = 1 |nx = 1 |=1 |
| |ny = 1 |ny = 1 |in other words, there is only one |
| |nz = 1 |nz = 1 |state => the ground state |
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