Einstein Coefficients - Laser Beams

AI Thread Summary
In a two-level laser system with no degeneracy, the relationship between the Einstein coefficients B12 and B21 is explored under the condition that the sum of populations N1 and N2 remains constant. The equations governing the time evolution of N1 and N2 suggest that their rates of change are influenced by the respective Einstein coefficients and the density of states. The discussion highlights a potential issue with the signs in the equations, indicating confusion in the application of conventions. The user seeks clarification on their approach and assistance with LaTeX formatting. Understanding the relationship between the coefficients is crucial for analyzing laser dynamics.
Ivor Denham
Messages
2
Reaction score
0

Homework Statement


Assume a two level laser system with no degeneracy (g1 = g2 = 1).
If N_2 + N1 = \text{constant}[\tex], show that B12 = B21[\tex].<br /> <br /> <h2>Homework Equations</h2><br /> \frac{\partial N_1}{\partial t}=-B_{12}\rho(v_{21}N_1[\tex]<br /> \frac{\partial N_2}{\partial t}=-B_{21}\rho(v_{21}N_2[\tex]<br /> <br /> <h2>The Attempt at a Solution</h2> <br /> I think there might be something up with the signs in the relevant equation, a convention I am not observing.<br /> <br /> N_1+N_2=c[\tex]<br /> <b>\frac{\partial N_1}{\partial t}+\frac{\partial N_2}{\partial t}=\frac{\partial c}{\partial t}[\tex]</b><br /> <b><b><b>\frac{\partial N_1}{\partial t}+\frac{\partial N_2}{\partial t}=0[\tex]</b></b><br /> <b><b><b><b><b><b>-B_{12}\rho(v_{21}N_1+-B_{21}\rho(v_{21}N_2=0[\tex]</b></b></b></b><br /> <b><b><b><b><b><b><b><b><b><b><b><b>-B_{12}N_1+-B_{21}N_2=0[\tex]</b></b></b></b></b></b></b></b><br /> <b><b><b><b><b><b><b><b><br /> From here I am stuck, where have I gone wrong?</b></b></b></b></b></b></b></b></b></b></b></b></b></b></b>[/B]
 
Physics news on Phys.org
Also could someone tell me how to fix the latex?
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Proving Snell's law using Euler-Lagrange equations
Replies
15
Views
6K
Two Level System with thermal population
Replies
1
Views
2K
I Ratio between spontaneous/stimulated emission
Replies
1
Views
13K
Understanding solution to equations of motion of n coupled oscillators
Replies
4
Views
2K
Calculating the Cross Section for a Laser's Transition Rate Equations
Replies
1
Views
2K
Terminal Velocity's Relationship to Mass
Replies
2
Views
3K
QM: Potential, Finite Step Function
Replies
6
Views
2K
Thermodynamics: Gradient of Adiabat in PV diagram
Replies
9
Views
3K
What Is Gain Narrowing in Lasers?
Replies
3
Views
5K
[Thermo.] thermal expansion and isothermal compressibility coefficients.
Replies
1
Views
7K

Hot Threads

Recent Insights

Back
Top