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.
See also:
- physics.stackexchange.com/questions/233330/why-do-electrons-jump-between-orbitals
- physics.stackexchange.com/questions/117417/quantum-mechanics-scattering-theory/522220#522220
- physics.stackexchange.com/questions/430268/stimulated-emission-how-can-giving-energy-to-electrons-make-them-decay-to-a-low/430288
TODO understand better, mentioned e.g. at Subtle is the Lord by Abraham Pais (1982) page 20, and is something that Einstein worked on.
Articles by others on the same topic
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.