Howtosignalprocessing
- What does translational invariance of space imply?
- What is translation in quantum mechanics?
- Is the translation operator linear?
- What is discrete time translation symmetry?
What does translational invariance of space imply?
Translational invariance implies that, at least in one direction, the object is infinite: for any given point p, the set of points with the same properties due to the translational symmetry form the infinite discrete set p + na | n ∈ Z = p + Z a.
What is translation in quantum mechanics?
In quantum mechanics, a translation operator is defined as an operator which shifts particles and fields by a certain amount in a certain direction. Translation operators are unitary. -component of the momentum operator.
Is the translation operator linear?
Translation operators are linear and unitary. They are closely related to the momentum operator; for example, a translation operator that moves by an infinitesimal amount in the x direction has a simple relationship to the x-component of the momentum operator.
What is discrete time translation symmetry?
Driving a system periodically establishes discrete time-translational symmetry. Much like graphite's repeating pattern of carbon atoms in space, periodic driving leads to a repeating pattern in time: The system's Hamiltonian returns to itself after every full driving period.
