By Debye P.

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A vector with unit length parallel to one of the axes of the coordinate system will be designated by a letter with a caret ( ) on top. In particular, x, y, and z denote unit vectors parallel to the x-, y- and z-axes of a Cartesian coordinate system. Matrices will be represented by non-italicized letters in boldface. We also will make frequent use of operators. An operator is just a recipe for a mathematical procedure that uses a given variable as input. We will designate an operator by a letter with a tilde (∼) on top, and indicate the input by a letter or other symbol immediately after the operator.

Born’s interpretation of the wavefunction puts restrictions on the mathematical functions that can be physically meaningful wavefunctions. First, Ψ must be a single-valued function of position. There should be only one value for the probability of finding a system at any given point. Second, the integral of Ψ ∗ Ψ dσ over any region of space must be finite; the probability of finding the system in any particular volume element should not go to infinity. Third, the integral Ψ|Ψ must exist and must be finite.

Probably the most useful form of Raman spectroscopy in molecular biophysics has been resonance Raman spectroscopy, in which the frequency of the excitation light is tuned to fall within an electronic absorption band. The electronic resonance has two benefits: it greatly increases the strength of the Raman scattering, and it can make the measurement specific for a chromophore with a particular electronic absorption spectrum. Resonance Raman scattering thus lends itself to probing the states of a ligand such as retinal or heme bound to a protein with little interference from the protein atoms.

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