Related papers: Teaching Quantum Mechanical Commutation Relations …
The canonical commutation relation is a cornerstone of quantum theory and underlies the Heisenberg uncertainty principle. Although uncertainty relations have been extensively tested, direct verifications of the underlying commutation…
Quantum mechanics is a field often considered very mathematical, abstract, and unintuitive. One way some instructors are hoping to help familiarize their students with these complex topics is to have the students see quantum effects in…
We study the commutation relations, uncertainty relations and spectra of position and momentum operators within the framework of quantum group % symmetric Heisenberg algebras and their (Bargmann-) Fock representations. As an effect of the…
As experiments continue to push the quantum-classical boundary using increasingly complex dynamical systems, the interpretation of experimental data becomes more and more challenging: when the observations are noisy, indirect, and limited,…
To learn quantum mechanics, one must become adept in the use of various mathematical structures that make up the theory; one must also become familiar with some basic laboratory experiments that the theory is designed to explain. The…
A common learning goal for modern physics instructors is for students to recognize a difference between the experimental uncertainty of classical physics and the fundamental uncertainty of quantum mechanics. Our studies suggest this…
We investigate the difficulties that undergraduate students in quantum mechanics courses have in transferring learning from previous courses or within the same course from one context to another by administering written tests and conducting…
Instruction in quantum mechanics is becoming increasingly important as the field is not only a key part of modern physics research, but is also important for emerging technologies. However, many students regard quantum mechanics as a…
Heisenberg's uncertainty principle implies fundamental constraints on what properties of a quantum system can we simultaneously learn. However, it typically assumes that we probe these properties via measurements at a single point in time.…
Quantum uncertainty relations have deep-rooted significance on the formalism of quantum mechanics. Heisenberg's uncertainty relations attracted a renewed interest for its applications in quantum information science. Robertson derived a…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…
A quantum mechanical model for the systems consisting of interacting bodies is considered. The model takes into account the noncommutativity of the space and impulse operators and the correlation equations for the indeterminacy of these…
The uncertainty relation of three quantities in quantum mechanics is estimated in terms of commutators. The Pauli matrices are used to find a contribution of third-order commutators. The resulting inequality refines the Heisenberg…
Quantum measurement and quantum operation theory is developed here by taking the relational properties among quantum systems, instead of the independent properties of a quantum system, as the most fundamental elements. By studying how the…
One of the main challenges in physics today is to merge quantum theory and the theory of general relativity into a unified framework. Various approaches towards developing such a theory of quantum gravity are pursued, but the lack of…
Our knowledge of quantum mechanics can satisfactorily describe simple, microscopic systems, but is yet to explain the macroscopic everyday phenomena we observe. Here we aim to shed some light on the quantum-to-classical transition as seen…
The usual conjectures of quantum measurements approaches, inspired from the traditional interpretation of Heisenberg's ("uncertainty") relations, are proved as being incorrect. A group of reconsidered conjectures and a corresponding new…
Many of the conceptual problems students have in understanding quantum mechanics arise from the way probabilities are introduced in standard (textbook) quantum theory through the use of measurements. Introducing consistent microscopic…
The ability to control the motion of mechanical systems through its interaction with light has opened the door to a plethora of applications in fundamental and applied physics. With experiments routinely reaching the quantum regime, the…