- #1
Higgsono
- 93
- 4
The multiplicity of states for a particle in a box is proportional to the product of the volume of the box and the surface area of momentum space.
$$ \Omega = V_{volume}V_{momentum}$$
The surface area in momentum space is given by the equation:
$$p^{2}_{x}+ {p}^{2}_{y}+{p}^{2}_{z} = \frac{U}{2m}$$
But this seem rediculous to me. It says that, "the number of possible directions a particle can travel in is proportional to the total energy of the particle". I don't understand this, why would the particle have more directions to choose from when it have higher energy? I know what the mathematics says, but the physics of it I don't understand.
$$ \Omega = V_{volume}V_{momentum}$$
The surface area in momentum space is given by the equation:
$$p^{2}_{x}+ {p}^{2}_{y}+{p}^{2}_{z} = \frac{U}{2m}$$
But this seem rediculous to me. It says that, "the number of possible directions a particle can travel in is proportional to the total energy of the particle". I don't understand this, why would the particle have more directions to choose from when it have higher energy? I know what the mathematics says, but the physics of it I don't understand.