Related papers: Common Misconceptions About Angular Momentum
Compared with introductory physics, relatively little is known about the development of expertise in advanced physics courses, especially in the case of quantum mechanics. Here, we describe a framework for understanding the patterns of…
The uncertainty principle places a fundamental limit on the accuracy with which we can measure conjugate physical quantities. However, the fluctuations of these variables can be assessed in terms of different estimators. We propose a new…
Waves of various types carry momentum, which is associated with their propagation direction, i.e., the phase gradient. The circulation of the wave momentum density gives rise to orbital angular momentum (AM). Additionally, for waves…
The subject of optomechanics involves interactions between optical and mechanical degrees of freedom, and is currently of great interest as an enabler of fundamental investigations in quantum mechanics, as well as a platform for…
Vacuum systems are an intrinsic part of any accelerator around the world: all particles circulate under vacuum. This lecture gives rudiments on the fundamentals of vacuum science such as units, ideal gas law, partial pressure, mean free…
Quantum mechanics can seem like a departure from everyday experience of the physical world, but constructivist theories assert that learners build new ideas from their existing ones. To explore how students can navigate this tension, we…
Classical mechanics involves position and momentum variables that must be special coordinates chosen to promote to suitable quantum operators. Since classical variables may be broadly chosen, only unique variables should be chosen. We will…
Multipolar solutions of Maxwell's equations are used in many practical applications and are essential for the understanding of light-matter interactions at the fundamental level. Unlike the set of plane wave solutions of electromagnetic…
In nonrelativistic quantum mechanics, the total (i.e. orbital plus spin) angular momentum of a charged particle with spin that moves in a Coulomb plus spin-orbit-coupling potential is conserved. In a classical nonrelativistic treatment of…
The goal of this book is to present classical mechanics, quantum mechanics, and statistical mechanics in an almost completely algebraic setting, thereby introducing mathematicians, physicists, and engineers to the ideas relating classical…
The study of the motion of a rigid body on a plane (RBP motion) is usually one of the most challenging topics that students face in introductory physics courses. In this paper, we discuss a couple of problems which are typically used in…
Students are taught several models of conductivity, both at the introductory and the advanced level. From early macroscopic models of current flow in circuits, through the discussion of microscopic particle descriptions of electrons flowing…
Electromagnetic waves with an azimuthal phase shift are known to have a well defined orbital angular momentum. Different methods that allow for the detection of the angular momentum are proposed. For some, we discuss the required…
The use of momentum in stochastic gradient methods has become a widespread practice in machine learning. Different variants of momentum, including heavy-ball momentum, Nesterov's accelerated gradient (NAG), and quasi-hyperbolic momentum…
While studying the motion of a heavy symmetric top, in general, constants of motion are used. Some students may want to understand the motion in terms of torque, which can lie on their routine based on the usage of Newton's second law.…
The Stern Gerlach experiment has played a central role in the discovery of spin angular momentum and it has also played a pivotal role in elucidating foundational issues in quantum mechanics. Here, we discuss investigation of students'…
Lecture notes for a one-semester master-level course on analytical mechanics and classical field theory, covering: 0 Mathematical Introduction, 1 Lagrangian Mechanics, 2 Application: Motion in Central Fields, 3 Hamiltonian Mechanics, 4…
This is a very gentle introductory course on quantum mechanics aimed at the first years of the undergraduate level. The basic concepts are introduced, with many applications and illustrations. Contains 12 short chapters of equal length,…
The well-known issue with the absence of conservation of angular momentum in classical particle systems with periodic boundary conditions is addressed. It is shown that conventional theory based on Noether's theorem fails to explain the…
The total angular momentum of light has received attention for its application in a variety of phenomena such as optical communication, optical forces and sensing. However, the quantum behavior including the commutation relations have been…