Keyword Analysis & Research: airy function quantum mechanics

wikipedia.org

https://en.wikipedia.org/wiki/Airy_function

In the physical sciences, the Airy function (or Airy function of the first kind) Ai(x) is a special function named after the British astronomer George Biddell Airy (1801–1892). The function Ai(x) and the related function Bi(x), are linearly independent solutions to the differential equation

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9to5science.com

https://9to5science.com/quantum-mechanics-and-the-airy-function-the-physics-of-the-turning-point

Jul 14, 2022 · Now turn to the quantum mechanic picture, or to be more exact to the semiclassical WKB method. One tries to approximate the quantum mechanic solution by some other functions. In the case of the Harmonic Oscillator these approximating functions are exactly the Airy functions (with some prefactors).

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wolfram.com

https://mathworld.wolfram.com/AiryFunctions.html

Aug 06, 2022 · There are four varieties of Airy functions: Ai(z), Bi(z), Gi(z), and Hi(z). Of these, Ai(z) and Bi(z) are by far the most common, with Gi(z) and Hi(z) being encountered much less frequently. Airy functions commonly appear in physics, especially in optics, quantum mechanics, electromagnetics, and radiative transfer.

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stackexchange.com

https://physics.stackexchange.com/questions/79959/quantum-mechanics-and-the-airy-function-the-physics-of-the-turning-point

Now turn to the quantum mechanic picture, or to be more exact to the semiclassical WKB method. One tries to approximate the quantum mechanic solution by some other functions. In the case of the Harmonic Oscillator these approximating functions are exactly the Airy functions (with some prefactors). Reviews: 1

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wolfram.com

https://functions.wolfram.com/Bessel-TypeFunctions/AiryAi/introductions/Airys/ShowAll.html

Applications of Airy functions Applications of Airy functions include quantum mechanics of linear potential, electrodynamics, electromagnetism, combinatorics, analysis of the algorithmic complexity, optical theory of the rainbow, solid state physics, radiative transfer, and semiconductors in electric fields.

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binghamton.edu

https://bingweb.binghamton.edu/~suzuki/QuantumMechanicsFiles/13-6%20Airy%20function%20for%20triangular%20potential.pdf

In the physical sciences, the Airy function (or Airy function of the first kind) Ai(x) is a special function named after the British astronomer George Biddell Airy (1801–1892). The function Ai(x) and the related function Bi(x), are linearly independent solutions to the differential equation 2 2 ( ) ( ) 0 dyx xyx dx , (1)

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analytica.com

https://wiki.analytica.com/index.php?title=Airy_functions

Airy functions are advanced mathematical functions that are typically denoted as $ Ai(x) $ and $ Bi(x) $ in scholarly articles. The are used in many fields including quantum mechanics, electrodynamics, electromagnetism, analysis of combinatory complexity, computation of orthogonal polynomials and spectra, optics, combinatorics, solid state physics, and the study …

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stackexchange.com

https://math.stackexchange.com/questions/4462989/where-does-the-airy-function-integral-representation-come-from

Jun 01, 2022 · Ψ ~ ( ω) = F { Ψ } = ∫ − ∞ ∞ Ψ ( x) e − i ω x d x. to the ODE, leads to the first order ODE − ω 2 Ψ ~ − i d Ψ ~ d ω = 0, thus. Ψ ~ = A e i ω 3 / 3. Substituting into the inverse transform results in the above form. Ψ ( x) = F − 1 Ψ ~ = A 2 π ∫ − ∞ ∞ e i ω 3 / 3 + i x ω d ω.

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