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Gaussian function: Quiz


Question 1: Mathematically, the derivatives of the Gaussian function can be represented using ________.
Hilbert spaceDirac delta functionOrthogonal polynomialsHermite polynomials

Question 2: The molecular orbitals used in computational chemistry can be linear combinations of Gaussian functions called Gaussian orbitals (see also ________).
Basis set (chemistry)Quantum chemistryMatrix (mathematics)Hartree–Fock method

Question 3: What does the following picture show?

  Normalized Gaussian curves with expected value μ and variance σ2. The corresponding parameters are a = 1/(σ√(2π)), b = μ, c = σ
  θ = π / 3
  Gaussian curve with a 2-dimensional domain
  θ = π / 3

Question 4: A Gaussian function is the wave function of the ground state of the ________.
Quantum harmonic oscillatorSchrödinger equationQuantum mechanicsQuantum field theory

Question 5: The convolution of a function with a Gaussian is also known as a ________.
Gaussian functionComplex numberFourier transformWeierstrass transform

Question 6: In statistics and probability theory, Gaussian functions appear as the density function of the normal distribution, which is a limiting probability distribution of complicated sums, according to the ________.
Characteristic function (probability theory)Multivariate normal distributionCentral limit theoremBinomial distribution

Question 7: Specifically, derivatives of Gaussians (________) are used as a basis for defining a large number of types of visual operations.
Orthogonal polynomialsHermite polynomialsDirac delta functionHilbert space

Question 8: The product of two Gaussian functions is not[citation needed] a Gaussian, and the ________ of two Gaussian functions is again a Gaussian.
Dirac delta functionConvolutionVector spaceFourier transform

Question 9: ________ are used in optical and microwave systems.
LaserElectromagnetic wave equationOpticsGaussian beam

Question 10: The Gaussian functions are thus those functions whose ________ is a quadratic function.
Group (mathematics)ExponentiationNatural logarithmLogarithm


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