Lecture

Rotating frame revisited

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Description

This lecture revisits the concept of the rotating frame in the context of biomedical imaging, exploring the equation of motion for magnetization in different reference frames and the implications of stationary magnetization. The quantum-mechanical equivalencies in the rotating frame are also discussed, focusing on the Schrödinger representation and determining various observables. The interaction representation and higher-order perturbation theory are introduced to split the Hamiltonian into time-invariant and -dependent terms, providing insights into the dynamics of spin-1/2 systems. Special attention is given to the determination of observables like and the role of the rotating frame in quantum mechanics.

In MOOC

Fundamentals of Biomedical Imaging: Magnetic Resonance Imaging (MRI)

This physics course covers the physical principles of major in vivo bio-imaging modalities. This course will focus on magnetic resonance imaging, also known as an MRI. In the first part of the course, the dynamic of spins in a magnetic field is described, leading to the essential notions of magnetic resonance (MR), excitation and relaxation. We will also discuss the basic mechanisms of image reconstruction, MR spectroscopy and functional MRI. You will learn how existing physical principles transcend into bi

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Related concepts (28)

Quantum mechanics

Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales.

Rotating reference frame

A rotating frame of reference is a special case of a non-inertial reference frame that is rotating relative to an inertial reference frame. An everyday example of a rotating reference frame is the surface of the Earth. (This article considers only frames rotating about a fixed axis. For more general rotations, see Euler angles.) Fictitious force All non-inertial reference frames exhibit fictitious forces; rotating reference frames are characterized by three: the centrifugal force, the Coriolis force, and, for non-uniformly rotating reference frames, the Euler force.

Non-inertial reference frame

A non-inertial reference frame is a frame of reference that undergoes acceleration with respect to an inertial frame. An accelerometer at rest in a non-inertial frame will, in general, detect a non-zero acceleration. While the laws of motion are the same in all inertial frames, in non-inertial frames, they vary from frame to frame depending on the acceleration. In classical mechanics it is often possible to explain the motion of bodies in non-inertial reference frames by introducing additional fictitious forces (also called inertial forces, pseudo-forces and d'Alembert forces) to Newton's second law.

Measurement in quantum mechanics

In quantum physics, a measurement is the testing or manipulation of a physical system to yield a numerical result. A fundamental feature of quantum theory is that the predictions it makes are probabilistic. The procedure for finding a probability involves combining a quantum state, which mathematically describes a quantum system, with a mathematical representation of the measurement to be performed on that system. The formula for this calculation is known as the Born rule.

Frame of reference

In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system whose origin, orientation, and scale are specified by a set of reference points―geometric points whose position is identified both mathematically (with numerical coordinate values) and physically (signaled by conventional markers). For n dimensions, n + 1 reference points are sufficient to fully define a reference frame.

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