- #1

- 4,807

- 32

There is another passage in Reif that got me really confused. It is in section 9.9 (Quantum states of a single particles).

We are considering an ideal gaz in a rectangular box of volume [itex]L_xL_yL_z=V[/itex] and we are making the approximation that the wave function of a particle of the gaz is that of a free particle that must have the lenghts of the box as a period. In other words, we say that

[tex]\psi(\vec{r})=e^{i\vec{k}\cdot \vec{r}}[/tex]

and we demand that

[tex]k_i=\frac{2\pi}{L_i}n_i, \ \ \ \ \ i=x,y,z, \ \ \ \ \ n_i \in \mathbb{Z}[/tex]

Reif then argues that for any macroscopic box, the L_i are large and thus, in a small interval [k_i,ki+dk_i] of the wave number, there are very many states of the particle (many n_i)...But I look at [itex]k_i=\frac{2\pi}{L_i}n_i[/itex] and wheter the ratio [itex]2\pi/L_i[/itex] is small depends heavily on the choice of units we use to measure distances.

We are considering an ideal gaz in a rectangular box of volume [itex]L_xL_yL_z=V[/itex] and we are making the approximation that the wave function of a particle of the gaz is that of a free particle that must have the lenghts of the box as a period. In other words, we say that

[tex]\psi(\vec{r})=e^{i\vec{k}\cdot \vec{r}}[/tex]

and we demand that

[tex]k_i=\frac{2\pi}{L_i}n_i, \ \ \ \ \ i=x,y,z, \ \ \ \ \ n_i \in \mathbb{Z}[/tex]

Reif then argues that for any macroscopic box, the L_i are large and thus, in a small interval [k_i,ki+dk_i] of the wave number, there are very many states of the particle (many n_i)...But I look at [itex]k_i=\frac{2\pi}{L_i}n_i[/itex] and wheter the ratio [itex]2\pi/L_i[/itex] is small depends heavily on the choice of units we use to measure distances.

Last edited: