 Spontaneous emission

Do electrons spontaneously jump from high orbitals to lower ones emitting photons?

Explaining this was was one of the key initial achievements of the Dirac equation.

Yes, but this is not predicted by the Schrödinger equation, you need to go to the Dirac equation.

A critical application of this phenomena is laser.

See also:

Spontaneous emission is a process by which an excited quantum system, such as an atom or a molecule, loses energy and transitions to a lower energy state without external influence. During this transition, the system emits a photon, which carries away energy and momentum. Key characteristics of spontaneous emission include: 1. **Randomness**: The process is inherently stochastic, meaning it occurs at random times and cannot be predicted exactly.