What's the difference between stimulated and spontaneous emission in lasers and diodes? I know that an LED emits light by spontaneous emission. To get more coherent  and Monochromatic light, we should use a laser.


*

*What is the reason that laser light is the most coherent and
Monochromatic?

*is there some equation  quantum mechanic ** or **solid state that
describe both of them? i explain more which equation in physics
describe these in form Mathematical? for example for a particle in
box i saw the solution QM for it. i want to finding equation and
solution for it.

*is there limitation in using for these  phenomenons for
creating nice laser?for example what nice laser we can create ? for
example we has limitation in efficiency thermodynamics  steam engine
we can not have any 100  efficiency,


i hope that i conveyed  my meaning.
 thank you
 A: Spontaneous emission does not require an external electromagnetic stimulus to release energy, whereas stimulated emission does require external electromagnetic stimuli to release energy.
• During spontaneous emission, only one energy wave is released, but during stimulated emission two energy waves are released.
• The probability of stimulated emission to take place is higher than the probability for spontaneous emission to take place as external electromagnetic stimuli increases the probability of attaining the dipole transition state.
• By properly matching the energy gaps and incident frequencies, stimulated emission can be used to greatly amplify the incident radiation beam; whereas this is not possible when spontaneous emission takes place.
A: You are taking these terms as binary conditions, which is never the case.  First of all, in a laser the initial state is zero photons.  It's only thru statistical emission (fluorescence) that any photons come into being.  The fraction of these photons which travel between the laser cavity mirror ends then stimulate further emission. At the same time, there is also fluorescence going on, so the trick (so to speak) is to set up the laser so that internal amplification leads to massive stimulated emission before the fluorescence lifetime "expires."
A non-laser source  starts with fluorescence as well, but depending on the physical conditions,  there can be some stimulated emissions as well.  Because there's no mirrors,  the ratio of stimulated to fluorescent emission is quite low.
Yes, there are certainly limits on laser quality.  Perhaps you can start by reading about the Einstein Relations, which describe how a laser works, and then move on to line broadening,  Lamb Dip, and other phenomena.
