But QP says that electrons have a wave function which gives it a probability of existing at several points. If we plot the probability of finding an electron in each space, we find that the highest probability of finding is around the classical circular orbit. But there’s some non-zero probability of finding it outside it too! We call this probability distribution as an “electron cloud”.
2. You cannot reach absolute zero temperature: We have learnt in school that there’s absolute zero temperature (-273 C). QP makes it impossible to reach absolute zero.
It’s because the temperature is essentially vibration of individual molecules. Absolute zero means that all the vibration stops and everything is at rest. But from the uncertainty principle of QP, we know that we can’t precisely measure the position of molecules. It means that they cannot be at absolute rest. There will be a little bit of motion. When there’s motion, there’s temperature!
You can go close to absolute zero, but cannot reach it.
3. Quantum Fluctuations: As discussed above, just like there is no “absolute position of rest” due to uncertainty, which results in fluctuation of “position” of molecules, a similar phenomenon happens in case of energy too.
As per CP, you look at empty space and can say that there’s zero energy. But QP doesn’t allow for “absolute zero” energy, there is always a fluctuation of energy. This is called quantum fluctuation.
4. Hawking radiation: From the famous E = mc^2 equation, we know that energy and mass are equivalent. If you have enough energy, you can get mass.
From QP, we know that there is always a fluctuation of energy. This quantum fluctuation sometimes results in the creation of “particle-antiparticle” pairs, which is often called as “particles popping in and out of existence”. These pairs annihilate themselves quickly.
Hawking applied this concept to blackhole. We know that there’s a boundary around the black hole, beyond which nothing can escape. Hawking argued that if such quantum fluctuation resulting in particle-antiparticle creation happens at the boundary of a black hole, there is a chance that one particle falls inside and other falls outside. Since the particle that fell inside can’t come out, the particle that fell outside will travel outwards, resulting in what we call “Hawking radiation”.
This has led to famous black hole information paradox.
5. Quantum leaking in semiconductors: If the energy of an object is X, CP says that it can’t overcome an energy barrier which is more than X. But QP talks of probabilities. It gives a non-zero probability of objects passing through the high energy barrier. We call it quantum tunnelling.
Quantum tunnelling is accounted for while making semiconductors because it results in “quantum leakage”.