1 dimensional crystal at rest, a nucleus emits gamma ray of energy E,

[Spinnor]

Say we have a one dimensional chain of N mass points separated by springs of spring constant k. This system can be quantized?

Let the quantized system above be at rest and let one of the end mass points emit a photon of energy E along the crystal axis. Will we get physics similar to he Mossbauer Effect where for small eneough energy E the photon emission would most likely cause the whole crystal to recoil with no phonons likely being produced?

Should it be straight forward quantum physics to determine the energy E of the photon that leads to a 50% chance of no phonons being produced?

If I give an impulse to the last mass point of the classical crystal above do I excite all the vibrational modes of the crystal?

Thanks for any help!

 

[mfb]

Say we have a one dimensional chain of N mass points separated by springs of spring constant k. This system can be quantized?

Let the quantized system above be at rest and let one of the end mass points emit a photon of energy E along the crystal axis. Will we get physics similar to he Mossbauer Effect where for small eneough energy E the photon emission would most likely cause the whole crystal to recoil with no phonons likely being produced?

Sure. Assuming your motion is restricted to one dimension, otherwise you have to care about rotation.

Should it be straight forward quantum physics to determine the energy E of the photon that leads to a 50% chance of no phonons being produced?

Probably not.

If I give an impulse to the last mass point of the classical crystal above do I excite all the vibrational modes of the crystal?

If the impulse is sufficient, I think so (all with some probability of course).