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Quantum energy is not real, but it's real

2 January 2024

https://www.youtube.com/watch?v=draPFwi8TQ4
(...) In this case of course we're looking at the total energy operator and this gives us a clue as to why our energy operator has an imaginary number in it. It's not that the energy of the system itself is imaginary, but rather the theoretical equivalent of measuring a particle's energy is applying this operator to its wave function. The result of applying this operator to the wave function is actually the energy of the system and this energy is very much real. It's not imaginary because remember, the whole point of energy is that it's this mathematical concept that allows us to work out how systems should behave and what they will tend to do in any given scenario. So then the question that comes up is how does an imaginary operator give us a real quantity which is the energy of the system? Well, the answer to this is that the wave function itself also has some imaginary part. It's a very hand wavy explanation but that's kind of basically what happens. Overall, applying this operator to the wave function gives us a real value which is very similar to the classical physics energy that we're already quite familiar with. (...) So let's recap. Is energy somehow weird and imaginary in the theory of quantum mechanics? No. (...)

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