"Non-relativistic" refers to a physical or mathematical description that does not take into account the effects of special relativity. Special relativity is a theory proposed by Albert Einstein that describes the behavior of objects moving at speeds close to the speed of light.
In non-relativistic systems, the speeds involved are much smaller compared to the speed of light, and the effects of special relativity can be neglected without significant loss of accuracy. Non-relativistic theories are often used to describe everyday objects and phenomena at normal speeds, such as those encountered in classical mechanics.
In the context of quantum mechanics, a non-relativistic theory is one that does not account for relativistic effects on particles, such as the increase in mass with velocity or the interplay between space and time. Non-relativistic quantum mechanics, also known as Schrödinger's quantum mechanics, is the formulation of quantum mechanics that is applicable to non-relativistic systems.
However, when dealing with high-energy particles or situations involving very fast speeds, relativistic effects become significant, and a non-relativistic description is inadequate. In such cases, one needs to employ relativistic theories, such as relativistic quantum mechanics or relativistic field theories, to accurately describe the behavior of particles and their interactions.