Q4Engineering Physics

In laser physics, Einstein's $A$ and $B$ coefficients mathematically describe strict quantum transition probabilities.

• $A_{21}$ (Spontaneous Emission): This rigidly represents the fundamental probability of a spontaneous downward quantum transition strictly per unit time. Therefore, its absolute dimensional unit is simply inverse time, ${\text{s}}^{-1}$.
• $B_{21}$ (Stimulated Emission): This mathematically represents the exact probability of a downward transition per unit time, specifically per unit spectral energy density ($\rho (\nu )$) of the stimulating external radiation field. Since $\rho (\nu )$ has units of $\text{J}\cdot \text{s}\cdot {\text{m}}^{-3}$, the absolute unit of $B_{21}$ rigorously becomes $\frac{{\text{s}}^{-1}}{\text{J}\cdot \text{s}\cdot {\text{m}}^{-3}}={\text{m}}^3\cdot {\text{J}}^{-1}\cdot {\text{s}}^{-2}$.