There is no doubt that one of the greatest scientific revolutions of the twentieth century was the Theory of Relativity proposed by** Albert Einstein**, whose ideas were fundamental to the development of the field of **quantum mechanics.**

In a simplistic way, it can be said that quantum mechanics is a branch of physics that deals with particles at the **atomic** and **subatomic** scale.

This is because, at such small scales, the general laws of classical mechanics, or Newtonian mechanics,** fail to explain the behavior** of these particles. Therefore, the task of calculating and predicting this behavior ends up being another challenge to physicists, because of its unpredictable nature.

However, from this study of particles’ behavior emerged **Quantum Statistics**, or statistics applied to quantum mechanics, which is a way of calculating the behavior of particles on a **quantum scale** when the general postulates of this branch of physics are not enough – for example when dealing with mixed ensembles.

In order to get a little bit closer to the statistical universe, we will show you some of the main concepts and applicability of this field of statistics. Stay here with us!

## Quantum Ensembles

The concept of Ensemble was created in 1902 by **J. W. Biggs** in the study of mechanics and thermodynamics.

An **ensemble, or statistical set**, is an abstraction in which one considers the large number of copies or probabilities of the system, where each copy represents a possibility of how the system can be in a phase or in evolution.

Given the number of different particles and behaviors within the same system, only from a mean of the sets, it would be possible to analyze their properties.

The **quantum ensemble**, therefore, applies when the particles of the set **become indistinguishable,** and the total energy E of the system is equally distributed among the unitary bodies. Here energy is also quantized, that is, it has no continuous values.

## Possible Results in Quantum Statistics

Within statistics applied to quantum mechanics, it is not possible **to speak of exact values**, but only probable results for the behavior of a quantum ensemble particle with an energy En.

This is because the entities are indistinguishable and **the calculation is probabilistic** within the set, determining the different ways in which the particle can behave.

In other words, there may be distinct effective results on a macroscopic scale when an experimenter is about to repeat an experiment, since it is not possible for the experimenter to control the actual behavior of the microscopic particles, but within the system, **the behaviors can be predictable with a certain probability.**

To sum up, in a simplified way, there is no way to predict how a particle will behave, but it is possible to predict **which behaviors are possible**. So, if the behaviors are as expected, it means that the experimenter’s tested hypothesis has been validated.

## Applications of Quantum Statistics

Quantum statistics is a field that requires deep study and research. It is from its results that particles such as the Higgs boson – known as the **God particle** – were theorized and proven to exist.

The chain of possibilities that Quantum Statistics brings ranges from a better understanding of how we see the universe to the possibility of generating **safer energies** from atomic fission.

Statistics applied to quantum mechanics is a complex subject, but at the same time it is fascinating for those who wish to unravel some of the hidden secrets of the universe, and to those who wish to be an expert in the field.

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