Do Quantum Mechanical States Have Definite Energies?

This is about quantum mechanics. If we are not doing measurement then it means system is not collapsing to a specific eigenstate. That means it is treated as superposition of all possible eigenstates. then how can be the energy of the system be defined in such kind of superposition? as it is not in the eigenstate corresponding to a specific energy. But logically it should possess a specific energy (well defined quantity of energy) all the time. What I expect is that although we are not doing any measurement, the system should possess definite amount of energy.
- Ashutosh (age 20)
Mumbai, India

Hi Ashutosh,

Your assumption (that states should have a well defined quantity of energy at every point in time) is very natural, but turns out to be experimentally false. As you said, physical states can be in superposition states of energies, in which case there is not a definite energy. (Usually we then talk about the expectation value of the energy.)

This same statement can be made about position, momentum, charge, etc: they don't always have definite values, as much as our classical intuition wants them to.

You might then worry about the conservation of energy. However, energy is still conserved, as hinted at here: https://van.physics.illinois.edu/qa/listing.php?id=24896. If you have two photons whose frequencies are entangled, then neither one has a definite energy, but their total energy adds up to a fixed value (equal to the energy that went into creating the two particles). So it works out fine.

David Schmid

(published on 07/25/2014)