Absorption and emission of photons Consider the following case:
An atom of hydrogen is in its ground state in vacuum. A single photon of light whose energy equals to the transition energy from the ground state( n=1) to the next energy level(n=2) is bombarded onto the atom. Now because the energy of the photon is same as that of the energy of the transition energy, the electron in the ground state will move to the next higher energy level. This is known as absorption. But because the total energy of the atom is higher it would want to go to a lower energy level. This is known as spontaneous emission. But the photon released in spontaneous emission is different from the photon initially bombarded( polarization, phase etc) but will have the same frequency. 
So here’s my question:


*

*Why does the emitted photon differ from the incoming photon?

*In laser the excited electron when bombarded with an photon emits 2 photons which have the same properties of the incoming photon. Why are the properties of the incoming photon and the outgoing photons the same?

 A: 
Why does the emitted photon differ from the incoming photon?

First, the emitted photon will be delayed by some time from when the first photon was absorbed.
Second, the emitted photon will be emitted in a random direction and polarization. Also, the phase of its associated EM wave will be random rather than coherent with the absorbed photon.

In laser the excited electron when bombarded with an photon emits 2 photons which have the same properties of the incoming photon.

This is not the usual way of looking at it. Usually we just say that there is no absorption process here --- the incoming photon continues without being changed, and one additional photon is emitted.

Why are the properties of the incoming photon and the outgoing photons the same?

Because this process is stimulated emission rather than spontaneous emission. The stimulated emission produces radiation that is coherent with the stimulating radiation.
A: In a laser the photon emission happens due to stimulated emission. Stimulated emission occurs when the electron is already in an excited state and an incident photon triggers the emission of an identical photon with the same frequency,  phase, and polarization as the incident photon. In spontaneous emission, no phase relation exists between the first photon that excited the electron to a higher energy level and the emitted photon. Spontaneous photon emission can only be described in the framework of quantum electrodynamics, where the interaction of the electron with the quantized electromagnetic field is described.
A: A post should only contain one question, so I ignore the second. The emitted photon generally has different properties from the absorbed if the atom at emission time is not (fully) coherent with itself at absorption time. So long as energy-momentum and angular momentum are conserved anything can then come out.
