# Energy of individual particles

• haael
In summary, in a Fock space with particles of one kind, there is an energy operator that acts on states and gives a value. The operator's behavior on single particle states is used to derive its action on the whole space. To measure individual particle energies, n energy operators can be defined in each n-particle sector. These operators do not interfere with each other and the non-interacting total energy operator is equal to the sum of one-particle energies. This is similar to how it is done in standard n-particle quantum mechanics.
haael
So OK, we have a Fock space of some particles of one kind.
Then we have energy operator that acts on the states and returns some value. The action of this operator on the whole space is derived from the behaviour on single particle states.

Now my question: how can we measure the energy of individual particles?

The energy operator only gives us the sum of all energies. We would have to define $$n$$ energy operators, one for each particle. How to do this so they not interfere with each other?

Yes, in each n-particle sector of the Fock space you can define n different energy operators - one for each particle. This is no different from how it is done in standard n-particle quantum mechanics. In this n-particle sector the non-interacting total energy operator

$$H = \int d^3p \omega_p a^{\dag}_pa_p$$

is exactly equal to the sum of n one-particle energies.

Eugene.

## What is the definition of energy of individual particles?

The energy of individual particles refers to the amount of energy possessed by a single particle, such as an atom or molecule.

## How is the energy of individual particles measured?

The energy of individual particles can be measured using various methods, such as spectroscopy, calorimetry, and particle accelerators.

## What factors affect the energy of individual particles?

The energy of individual particles can be affected by factors such as temperature, pressure, and the surrounding environment.

## How does the energy of individual particles contribute to physical and chemical processes?

The energy of individual particles plays a crucial role in physical and chemical processes, such as phase changes, chemical reactions, and nuclear reactions.

## Can the energy of individual particles be harnessed for practical use?

Yes, the energy of individual particles can be harnessed for practical use in various technologies, such as nuclear power plants, solar panels, and batteries.

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