The phrase "at the quantum level" is correct and usable in written English.
It can be used when discussing phenomena, theories, or concepts that pertain to quantum mechanics or the behavior of particles at a subatomic scale.
Example: "The behavior of electrons can be quite unpredictable at the quantum level, leading to fascinating implications for modern physics."
Alternatives: "on a quantum scale" or "at the subatomic level".
Which is when, well, you have to suspect that something is up at the quantum level.
Now a group of French scientists are trying to determine whether the same holds true even at the quantum level.
Representing a unitary transformation as an object makes it fairly simple to translate programming directives at the classical level into physical control instructions at the quantum level.
Indeterminism is supported to some extent by research in quantum mechanics, which suggests that some events at the quantum level are in principle unpredictable (and therefore random).
This is the part of physics concerned with the interaction between light and matter at the quantum level, so between individual particles of light, photons, and matter, such as atoms or ions (which are atoms but with electrons missing).
This is the most complete mathematical description physicists have of the universe at the quantum level and describes 12 particles of matter (called fermions) and 12 force-carrying particles (called bosons), in addition to their antimatter partners.
In the case of the valence band, the quantum levels appear at ε n below E V. The calculated quantum levels were added in Fig. 5.
Nagel's examples include a performance by a pianist - a description of every event in the performance at the quantum physical level, or possibly even at the muscular physiological level, would be overwhelmingly complex.
The diffusion of Li+ ions (atoms) and their interaction with the carbon materials are treated at the quantum mechanical level.
Plants, algae, and photosynthetic bacteria use surprisingly sophisticated optimizations at the quantum mechanical level to harvest the sun's energy.
In particular, we will show how molecular modelling at the quantum mechanics level is key for revealing the mechanistic details of catalysis in bacterial and viral metallo-enzymes.
