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A molecule in the gas phase is free to rotate relative to a set of mutually orthogonal axes of fixed orientation in space, centered on the center of mass of the molecule. Free rotation is not possible for molecules in liquid or solid phases due to the presence of intermolecular forces. Rotation about each unique axis is associated with a set of ...
One example of Rabi flopping is the spin flipping within a quantum system containing a spin-1/2 particle and an oscillating magnetic field. We split the magnetic field into a constant 'environment' field, and the oscillating part, so that our field looks like = + = + ( + ()) where and are the strengths of the environment and the oscillating fields respectively, and is the frequency at ...
Again, a finite rotation can be made from many small rotations, replacing Δθ by Δθ/N and taking the limit as N tends to infinity gives the rotation operator for a finite rotation. Rotations about the same axis do commute, for example a rotation through angles θ 1 and θ 2 about axis i can be written
In a magnetic field, even substances that lack chirality rotate the plane of polarized light, as shown by Michael Faraday. Magnetic optical rotation is known as the Faraday effect, and its wavelength dependence is known as magnetic optical rotatory dispersion. In regions of absorption, magnetic circular dichroism is observable.
The standard translational model of Brownian motion. Much like translational diffusion in which particles in one area of high concentration slowly spread position through random walks until they are near-equally distributed over the entire space, in rotational diffusion, over long periods of time the directions which these particles face will spread until they follow a completely random ...
Kerr rotation and Kerr ellipticity are changes in the polarization of incident light which comes in contact with a gyromagnetic material. Kerr rotation is a rotation in the plane of polarization of transmitted light, and Kerr ellipticity is the ratio of the major to minor axis of the ellipse traced out by elliptically polarized light on the plane through which it propagates.
Symbolically, the rotation invariance of a real-valued function of two real variables is f ( x ′ ) = f ( R x ) = f ( x ) {\displaystyle f(\mathbf {x} ')=f(\mathbf {Rx} )=f(\mathbf {x} )} In words, the function of the rotated coordinates takes exactly the same form as it did with the initial coordinates, the only difference is the rotated ...
This can be interpreted as a rotation of the time axis into the z axis, with an imaginary rotation parameter. If this rotation parameter were real, it would be possible for a 180° rotation to reverse the direction of time and of z. Reversing the direction of one axis is a reflection of space in any number of dimensions.