Quantum particles, like electrons or photons, are typically described as existing in a three-dimensional space. In the framework of classical quantum mechanics, these particles are treated as point-like entities occupying a position in three spatial dimensions.
The position of a quantum particle can be measured through various experimental techniques. For example, in the case of an electron, its position can be probed using devices such as electron microscopes or particle detectors. These measurements provide information about the particle's location in space within the limits of the measurement precision.
However, it's important to note that quantum mechanics introduces certain fundamental limitations to the measurement of a particle's position. The Heisenberg uncertainty principle states that there is a fundamental trade-off between the precision with which the position of a particle can be measured and the precision with which its momentum can be known. This means that the more precisely one tries to measure the position of a particle, the less precisely its momentum can be determined, and vice versa.
This uncertainty arises due to the wave-particle duality of quantum particles. Instead of having a definite position and momentum like classical objects, quantum particles can exhibit wave-like properties and can be described by a probability distribution called a wavefunction. The wavefunction contains information about the possible positions of the particle and the probabilities of finding it in different locations.
In summary, quantum particles are considered to exist in three dimensions, and their positions can be measured to some extent. However, the Heisenberg uncertainty principle imposes limitations on the precise simultaneous measurement of both position and momentum, introducing inherent uncertainties in the measurements.