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38 relations: Complex conjugate, Dirac delta function, Eigenvalues and eigenvectors, Exponential function, Fixed-point combinator, Fourier series, Function (mathematics), Function space, Gram–Schmidt process, Hamiltonian (quantum mechanics), Harmonic, Hermitian matrix, Hilbert space, Hilbert–Schmidt theorem, Identity matrix, Infinitesimal, Inner product space, Kronecker delta, Laplace operator, Linear map, Linear time-invariant theory, Mathematics, Orthonormal basis, Overtone, Partial differential equation, Quantum mechanics, Scalar (mathematics), Schrödinger equation, Self-adjoint operator, Separation of variables, Spectral theory of ordinary differential equations, Spectrum (functional analysis), Stationary state, String instrument, String vibration, Sturm–Liouville theory, Wave equation, Wave function.
Complex conjugate
In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign.
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Dirac delta function
In mathematics, the Dirac delta function (function) is a generalized function or distribution introduced by the physicist Paul Dirac.
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Eigenvalues and eigenvectors
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.
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Exponential function
In mathematics, an exponential function is a function of the form in which the argument occurs as an exponent.
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Fixed-point combinator
In computer science's combinatory logic, a fixed-point combinator (or fixpoint combinator) is a higher-order function fix that, for any function f that has an attractive fixed point, returns a fixed point x of that function.
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Fourier series
In mathematics, a Fourier series is a way to represent a function as the sum of simple sine waves.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Function space
In mathematics, a function space is a set of functions between two fixed sets.
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Gram–Schmidt process
In mathematics, particularly linear algebra and numerical analysis, the Gram–Schmidt process is a method for orthonormalising a set of vectors in an inner product space, most commonly the Euclidean space Rn equipped with the standard inner product.
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Hamiltonian (quantum mechanics)
In quantum mechanics, a Hamiltonian is an operator corresponding to the total energy of the system in most of the cases.
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Harmonic
A harmonic is any member of the harmonic series, a divergent infinite series.
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Hermitian matrix
In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the -th row and -th column is equal to the complex conjugate of the element in the -th row and -th column, for all indices and: Hermitian matrices can be understood as the complex extension of real symmetric matrices.
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Hilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.
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Hilbert–Schmidt theorem
In mathematical analysis, the Hilbert–Schmidt theorem, also known as the eigenfunction expansion theorem, is a fundamental result concerning compact, self-adjoint operators on Hilbert spaces.
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Identity matrix
In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.
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Infinitesimal
In mathematics, infinitesimals are things so small that there is no way to measure them.
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Inner product space
In linear algebra, an inner product space is a vector space with an additional structure called an inner product.
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Kronecker delta
In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers.
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Laplace operator
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a function on Euclidean space.
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Linear map
In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.
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Linear time-invariant theory
Linear time-invariant theory, commonly known as LTI system theory, comes from applied mathematics and has direct applications in NMR spectroscopy, seismology, circuits, signal processing, control theory, and other technical areas.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Orthonormal basis
In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for V whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other.
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Overtone
An overtone is any frequency greater than the fundamental frequency of a sound.
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Partial differential equation
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.
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Quantum mechanics
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
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Scalar (mathematics)
A scalar is an element of a field which is used to define a vector space.
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Schrödinger equation
In quantum mechanics, the Schrödinger equation is a mathematical equation that describes the changes over time of a physical system in which quantum effects, such as wave–particle duality, are significant.
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Self-adjoint operator
In mathematics, a self-adjoint operator on a finite-dimensional complex vector space V with inner product \langle\cdot,\cdot\rangle is a linear map A (from V to itself) that is its own adjoint: \langle Av,w\rangle.
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Separation of variables
In mathematics, separation of variables (also known as the Fourier method) is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation.
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Spectral theory of ordinary differential equations
In mathematics, the spectral theory of ordinary differential equations is the part of spectral theory concerned with the determination of the spectrum and eigenfunction expansion associated with a linear ordinary differential equation.
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Spectrum (functional analysis)
In mathematics, particularly in functional analysis, the spectrum of a bounded operator is a generalisation of the set of eigenvalues of a matrix.
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Stationary state
A stationary state is a quantum state with all observables independent of time.
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String instrument
String instruments, stringed instruments, or chordophones are musical instruments that produce sound from vibrating strings when the performer plays or sounds the strings in some manner.
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String vibration
A vibration in a string is a wave.
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Sturm–Liouville theory
In mathematics and its applications, a classical Sturm–Liouville theory, named after Jacques Charles François Sturm (1803–1855) and Joseph Liouville (1809–1882), is the theory of a real second-order linear differential equation of the form where y is a function of the free variable x. Here the functions p(x), q(x), and w(x) > 0 are specified at the outset.
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Wave equation
The wave equation is an important second-order linear partial differential equation for the description of waves—as they occur in classical physics—such as mechanical waves (e.g. water waves, sound waves and seismic waves) or light waves.
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Wave function
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system.
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References
[1] https://en.wikipedia.org/wiki/Eigenfunction
