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Using the Beer–Lambert law, the equation can be rewritten with the absorption coefficients and concentrations of each component. Δ A = ε HG [ HG ] b + ε G [ G ] b − ε G [ G ] 0 b {\displaystyle {\Delta }A=\varepsilon ^{\ce {HG}}[{\ce {HG}}]b+\varepsilon ^{\ce {G}}[{\ce {G}}]b-\varepsilon ^{\ce {G}}[{\ce {G}}]_{0}b\,}
Several phenomena have the same behavior as quantum tunnelling. Two examples are evanescent wave coupling (the application of Maxwell's wave-equation to light) and the application of the non-dispersive wave-equation from acoustics applied to "waves on strings". [citation needed] These effects are modeled similarly to the rectangular potential ...
Prentice's rule, named so after the optician Charles F. Prentice, is a formula used to determine the amount of induced prism in a lens: = where: P is the amount of prism correction (in prism dioptres) c is decentration (the distance between the pupil centre and the lens's optical centre, in millimetres)
Planck–Einstein equation and de Broglie wavelength relations. P = ( E/c, p) is the four-momentum, K = (ω/ c, k) is the four-wavevector, E = energy of particle. ω = 2π f is the angular frequency and frequency of the particle. ħ = h /2π are the Planck constants. c = speed of light. Schrödinger equation.
Linearity. The Schrödinger equation is a linear differential equation, meaning that if two state vectors and are solutions, then so is any linear combination. of the two state vectors where a and b are any complex numbers. [13] : 25 Moreover, the sum can be extended for any number of state vectors.
The Eyring equation (occasionally also known as Eyring–Polanyi equation) is an equation used in chemical kinetics to describe changes in the rate of a chemical reaction against temperature. It was developed almost simultaneously in 1935 by Henry Eyring, Meredith Gwynne Evans and Michael Polanyi.
The Van 't Hoff equation relates the change in the equilibrium constant, Keq, of a chemical reaction to the change in temperature, T, given the standard enthalpy change, ΔrH⊖, for the process. The subscript means "reaction" and the superscript means "standard". It was proposed by Dutch chemist Jacobus Henricus van 't Hoff in 1884 in his book ...
The result for two conducting spheres in a solvent is the formula of Marcus G = ( 1 2 r 1 + 1 2 r 2 − 1 R ) ⋅ ( 1 ϵ opt − 1 ϵ s ) ⋅ ( Δ e ) 2 {\displaystyle G=\left({\frac {1}{2r_{1}}}+{\frac {1}{2r_{2}}}-{\frac {1}{R}}\right)\cdot \left({\frac {1}{\epsilon _{\text{opt}}}}-{\frac {1}{\epsilon _{\text{s}}}}\right)\cdot (\Delta e)^{2}}
Some examples are positronium (bound state of an electron–positron pair), excitons (bound states of an electron–hole pairs), and mesons (as quark-antiquark bound states). Even for simple systems such as the positronium, the equation cannot be solved exactly, although in principle it can be formulated exactly.
Schröder's equation is an eigenvalue equation for the composition operator Ch that sends a function f to f(h(.)) . If a is a fixed point of h, meaning h(a) = a, then either Ψ (a) = 0 (or ∞) or s = 1. Thus, provided that Ψ (a) is finite and Ψ′ (a) does not vanish or diverge, the eigenvalue s is given by s = h′ (a) .