What is the transition probability in quantum mechanics?OPTIONS Probability of a system reaching absolute zero temperature Probability of a system transitioning from one energy state to another Probability of a photon escaping a black hole Probability of an electron changing its spin

Spontaneous transition probability depends ona.Lifetime of upper energy stateb.Independent of lifetimec.Lifetime of lower energy state

Spontaneous transition depends ona.Energy of input photonsb.Lifetime of excited statec.Number of atoms in ground state

The —---- describe the probability of observing an output given a hidden state.Select one:a. emission probabilitiesb. transition probabilities

If an excited state of an atom is known to have a lifetime of 10's, what is the uncertainty in the energy of photons emitted by such atoms in the spontaneous decay to the ground state?

Hawking’s discovery of the Hawking radiation, possible through thought experiment, brought general relativity and quantum theory together in a remarkable way. But Hawking was puzzled by features of this radiation – or more precisely, its lack of features. Critical to the probability interpretation of quantum mechanics was that something always happens. If you add up the probabilities for anything that may happen, you will find that the total probability is one. This can be formulated as a statement about information: if one knows everything one can know about a system at one time, one can know everything about it at later times. But this did not seem to be the case for radiation from black holes.These ideas may be unfamiliar – so it is worth elaborating a bit. If you enter a lottery and buy one ticket and there are 10 million lottery tickets sold, your chances of winning the jackpot are 1 in 10 million. But you either win or lose the lottery: the chance of winning or losing is 100 per cent.What does it mean for information to disappear? Of course, we all forget things… but we believe that we could, in time, reconstruct this information. The amount of information in a system doesn’t change, though it may be hard to access. For a system, like a collapsing star, there is a lot of information. …Thanks to Hawking, we know that it forms a black hole and then slowly evaporates, emitting radiation. The information that was contained in the initial star has been reduced to just the temperature of a warm body. Hawking argued that the information was simply lost. Quantum mechanics, he asserted, breaks down near black holes.Many leading theorists have struggled to resolve the puzzles raised by this thought experiment. Some have argued that, one has to redo quantum mechanics or general relativity to resolve Hawking’s paradox. Others have been more sceptical. Perhaps, the evaporation of a black hole is like a lump of ash from the burning of a log. Surely, the laws of quantum mechanics don’t break down when an object burns? In that case, the resolution of the puzzle is that the outgoing radiation is not exactly that of a black body because subtle connections between the outgoing photons remain intact. But it was soon realised that the answer could not be so simple; the structure of space and time makes it hard to understand how such correlations might arise. … Perhaps Hawking was right: just as Newtonian physics was usurped by quantum mechanics and general relativity on large or tiny scales, something had to give here as well.It turns out that there is a situation where black holes could exist and quantum mechanics could make sense: string theory. String theory, also emerging from thought experiments, replaces the particles of quantum mechanics with one-dimensional strings. That concept has provided at least a partial resolution of the puzzle. Two theorists at Harvard University – Cumrun Vafa and Andrew Strominger were able to understand the temperature of certain idealised black holes in quantum mechanical terms. In other words, the information, at least for these idealised systems, somehow survives, evading Hawking’s paradox.