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Topics referred to by the same term
Psi function can refer, in mathematics, to the ordinal collapsing function ψ ( α ) {\displaystyle \psi (\alpha )} the Dedekind psi function ψ ( n ) {\displaystyle
Psi_function
Mathematical function
digamma function is defined as the logarithmic derivative of the gamma function: ψ ( z ) = d d z ln Γ ( z ) = Γ ′ ( z ) Γ ( z ) . {\displaystyle \psi (z)={\frac
Digamma_function
Arithmetical function
Dedekind psi function is the multiplicative function on the positive integers defined by ψ ( n ) = n ∏ p | n ( 1 + 1 p ) , {\displaystyle \psi (n)=n\prod
Dedekind_psi_function
Buchholz's psi-functions are a hierarchy of single-argument ordinal functions ψ ν ( α ) {\displaystyle \psi _{\nu }(\alpha )} introduced by German mathematician
Buchholz_psi_functions
Set-theoretic function
countable, ψ {\displaystyle \psi } will "collapse" them to countable ordinals. To clarify how the function ψ {\displaystyle \psi } is able to produce notations
Ordinal_collapsing_function
Mathematical description of quantum state
system. The most common symbols for a wave function are the Greek letters ψ and Ψ (lower-case and capital psi, respectively). According to the superposition
Wave_function
Mathematical function relating circular and hyperbolic functions
In mathematics, the Gudermannian function relates a hyperbolic angle measure ψ {\textstyle \psi } to a circular angle measure ϕ {\textstyle \phi } called
Gudermannian_function
Generalisation of the generalised hypergeometric function pFq(z)
mathematics, the Fox–Wright function (also known as Fox–Wright Psi function, not to be confused with Wright Omega function) is a generalisation of the
Fox–Wright_function
Penultimate letter in the Greek alphabet
Psi /ˈ(p)saɪ, ˈ(p)siː/ (P)SY, (P)SEE (uppercase Ψ, lowercase ψ or 𝛙; Greek: ψι psi [ˈpsi]) is the twenty-third and penultimate letter of the Greek alphabet
Psi_(Greek)
Meromorphic function
the logarithm of the gamma function: ψ ( m ) ( z ) := d m d z m ψ ( z ) = d m + 1 d z m + 1 ln Γ ( z ) . {\displaystyle \psi ^{(m)}(z):={\frac {\mathrm
Polygamma_function
In mathematics, Rathjen's ψ {\displaystyle \psi } psi function is an ordinal collapsing function developed by Michael Rathjen. It collapses weakly Mahlo
Rathjen's_psi_function
Mathematical function
(n)=\int _{2}^{x}{\frac {\psi (t)\,dt}{t\log ^{2}t}}+{\frac {\psi (x)}{\log x}}.} The transition from Π to the prime-counting function, π, is made through the
Chebyshev_function
Mathematical function
ψ ( z ) {\displaystyle \psi _{1}(z)={\frac {d}{dz}}\psi (z)} where ψ(z) is the digamma function. It may also be defined as the sum of the series ψ 1
Trigamma_function
Method of solution to differential equations
In mathematics, a Green's function (or Green function) is the impulse response of an inhomogeneous linear differential operator defined on a domain with
Green's_function
Topics referred to by the same term
Look up PSI, Psi, or psi in Wiktionary, the free dictionary. Psi, PSI or Ψ may refer to: Psi (Greek) (Ψ or ψ), the twenty-third letter of the Greek alphabet
Psi
Description of a quantum-mechanical system
represent physical states. Thus, a position-space wave function Ψ ( x , t ) {\displaystyle \Psi (x,t)} as used above can be written as the inner product
Schrödinger_equation
Smooth and compactly supported function
terms "bump function" and "test function" are not synonymous in all contexts. The function Ψ : R → R {\displaystyle \Psi :\mathbb {R} \to \mathbb {R} }
Bump_function
Function whose domain is the positive integers
{\displaystyle \psi (x)=\sum _{p^{k}\leq x}\log p.} The second Chebyshev function ψ(x) is the summation function of the von Mangoldt function just below.
Arithmetic_function
Analytic function in mathematics
{1}{2}}\left(\psi ^{0}(t)+\psi ^{0}(-t)\right)-\gamma } with |t| < 2 and where ψ {\displaystyle \psi } and γ {\displaystyle \gamma } are the polygamma function and
Riemann_zeta_function
Fundamental theorem in condensed matter physics
in 1929. Mathematically, they are written Bloch function ψ ( r ) = e i k ⋅ r u ( r ) {\displaystyle \psi (\mathbf {r} )=e^{i\mathbf {k} \cdot \mathbf {r}
Bloch's_theorem
Type of statistics
know its ψ {\displaystyle \psi } function. I F ( x ; T , F ) = M − 1 ψ ( x , T ( F ) ) {\displaystyle IF(x;T,F)=M^{-1}\psi (x,T(F))} with the p × p {\displaystyle
Robust_statistics
Process by which a quantum system takes on a definitive state
interpretations of quantum mechanics, wave function collapse, also called reduction of the state vector, occurs when a wave function—initially in a superposition of
Wave_function_collapse
Large countable ordinal
ordinal, which acts as the limit of the range of Buchholz's psi function and Feferman's theta function. It was named by David Madore, after Gaisi Takeuti, Solomon
Takeuti–Feferman–Buchholz ordinal
Takeuti–Feferman–Buchholz_ordinal
Calculation rule in quantum mechanics
an observable, measured in a system with normalized wave function | ψ ⟩ {\displaystyle |\psi \rangle } (see Bra–ket notation), corresponds to a self-adjoint
Born_rule
Function for incompressible divergence-free flows in two dimensions
Batchelor define the stream function ψ {\displaystyle \psi } as follows. ψ ( x , y , t ) = ∫ A P ( u d y − v d x ) {\displaystyle \psi (x,y,t)=\int _{A}^{P}\left(u\
Stream_function
Number of integers coprime to and less than n
product of the first 120569 primes. Carmichael function (λ) Dedekind psi function (𝜓) Divisor function (σ) Duffin–Schaeffer conjecture Generalizations
Euler's_totient_function
Thought experiment in quantum mechanics
the meantime. Even a single atomic decay would have poisoned it. The psi-function of the entire system would express this by having in it the living and
Schrödinger's_cat
Probability distribution
[\ln(1-X)])^{2}\\&=\psi _{1}(\beta )-\psi _{1}(\alpha +\beta )\\&=\psi _{1}(\beta )+\operatorname {cov} [\ln X,\ln(1-X)]\end{aligned}}} where the trigamma function, denoted
Beta_distribution
Probability distribution
z)={}_{1}\Psi _{1}\left({\begin{matrix}\left(\alpha ,{\frac {1}{2}}\right)\\(1,0)\end{matrix}};z\right)} denotes the Fox–Wright Psi function. Normally
Normal_distribution
Type of mathematical function
In mathematical logic and set theory, an ordinal notation is a partial function mapping the set of all finite sequences of symbols, themselves members
Ordinal_notation
Correlators of field operators
ψ ( x , τ ) {\displaystyle \psi (\mathbf {x} ,\tau )} .] In real time, the 2 n {\displaystyle 2n} -point Green function is defined by G ( n ) ( 1 … n
Green's function (many-body theory)
Green's_function_(many-body_theory)
Probability distribution
denotes the Fox–Wright Psi function. The connection between the normalizing constant of the distribution and the Fox–Wright function in provided in Sun,
Modified half-normal distribution
Modified_half-normal_distribution
Russian cryptographic hash function
{\displaystyle \psi ^{i}} denotes an i-th power of the ψ {\displaystyle \psi } function. There are two commonly used sets of initial parameters for GOST R 34
GOST_(hash_function)
Extension of the factorial function
x)}{2\pi }}\left\{\psi \left({\dfrac {x}{2}}\right)-\psi \left({\dfrac {x+1}{2}}\right)\right\}\right],} where ψ(x) denotes the digamma function, and L {\displaystyle
Hadamard's_gamma_function
Description of physical properties at the atomic and subatomic scale
\psi (0)} – it makes a definite prediction of what the quantum state ψ ( t ) {\displaystyle \psi (t)} will be at any later time. Some wave functions produce
Quantum_mechanics
Product of numbers from 1 to n
Robert 2000. "7.1: The gamma function Γ p {\displaystyle \Gamma _{p}} ". pp. 366–385. Ross, Bertram (1978). "The psi function". Mathematics Magazine. 51
Factorial
Historically African-American fraternity
Omega Psi Phi Fraternity, Inc. (ΩΨΦ) is a historically African American fraternity. It was founded on November 17, 1911 at Howard University in Washington
Omega_Psi_Phi
Science fiction theme of 1950s and 1960s
extrasensory perception, telepathy and psychokinesis. The term is a blend word of psi (in the sense of "psychic phenomena") and the -onics from electronics. The
Psionics
Function in fluid dynamics
components uρ and uz can be expressed in terms of the Stokes stream function Ψ {\displaystyle \Psi } by: u ρ = − 1 ρ ∂ Ψ ∂ z , u z = + 1 ρ ∂ Ψ ∂ ρ . {\displaystyle
Stokes_stream_function
2004 video game
Psi-Ops: The Mindgate Conspiracy is a 2004 action-adventure video game developed by Midway for the Xbox, PlayStation 2, and Microsoft Windows. The game
Psi-Ops: The Mindgate Conspiracy
Psi-Ops:_The_Mindgate_Conspiracy
Mathematical entity to describe the probability of each possible measurement on a system
(x)|^{2}dx,} where | ψ ( x ) | 2 {\displaystyle |\psi (x)|^{2}} is the probability density function for finding a particle at a given position. These
Quantum_state
Ordinals in mathematics and set theory
value is equal to Ψ ( ε K + 1 ) {\displaystyle \Psi (\varepsilon _{K+1})} using Rathjen's Psi function. Next is another unnamed ordinal, referred by David
Large_countable_ordinal
Topics referred to by the same term
function can refer to any of three functions, all introduced by Richard Dedekind Dedekind eta function Dedekind psi function Dedekind zeta function This
Dedekind_function
Mathematical function
z_{n})\left(\psi (z_{m})-\psi {\left(\sum _{k=1}^{n}z_{k}\right)}\right),\quad 1\leq m\leq n,} where ψ ( z ) {\displaystyle \psi (z)} denotes the digamma function
Beta_function
{\displaystyle -\psi ''+V\psi =k^{2}\psi } . It was introduced by Res Jost. We are looking for solutions ψ ( k , r ) {\displaystyle \psi (k,r)} to the radial
Jost_function
North American collegiate fraternity
Psi Upsilon (ΨΥ), commonly known as Psi U, is a North American fraternity, founded at Union College on November 24, 1833. The fraternity has chartered
Psi_Upsilon
Function describing an electron in an atom
mechanics, an atomic orbital is a function describing the location and wave-like behavior of an electron in an atom. This function describes an electron's charge
Atomic_orbital
Pictorial representation of the behavior of subatomic particles
{\psi }}M\psi +{\bar {\eta }}\psi +{\bar {\psi }}\eta }\,D{\bar {\psi }}\,D\psi =\int e^{\left({\bar {\psi }}+{\bar {\eta }}M^{-1}\right)M\left(\psi +M^{-1}\eta
Feynman_diagram
Polynomial sequence
e^{-ikx}\psi _{n}(x)dx=(-i)^{n}\psi _{n}(k),\quad {\frac {1}{\sqrt {2\pi }}}\int e^{+ikx}\psi _{n}(k)dk=i^{n}\psi _{n}(x)} The Wigner distribution function of
Hermite_polynomials
Arithmetical function
{\frac {n^{k}}{\zeta (k+1)}}} . The Dedekind psi function is ψ ( n ) = J 2 ( n ) J 1 ( n ) {\displaystyle \psi (n)={\frac {J_{2}(n)}{J_{1}(n)}}} , and by
Jordan's_totient_function
Function on an integer n which is log(p) if n equals p^k and zero otherwise
> σ0. The second Chebyshev function ψ ( x ) {\displaystyle \psi (x)} is the summatory function of the von Mangoldt function: ψ ( x ) = ∑ p k ≤ x log
Von_Mangoldt_function
- wave function of the state of the system Ψ {\displaystyle \Psi } - total wave function of a system ψ {\displaystyle \psi } - wave function of a system
Glossary of elementary quantum mechanics
Glossary_of_elementary_quantum_mechanics
Foundational principle in quantum physics
time-independent wave function of a single-moded plane wave of wavenumber k0 or momentum p0 is ψ ( x ) ∝ e i k 0 x = e i p 0 x / ℏ . {\displaystyle \psi (x)\propto
Uncertainty_principle
Mathematical functions which are smooth but not analytic
natural number n (including zero) the smooth function ψ n ( x ) = x n h ( x ) , x ∈ R , {\displaystyle \psi _{n}(x)=x^{n}\,h(x),\qquad x\in \mathbb {R}
Non-analytic_smooth_function
Mathematical tool in quantum physics
_{-\infty }^{\infty }\psi ^{*}(x+y)\psi (x-y)e^{2ipy/\hbar }\,dy.} The equation for the time evolution of the Wigner function, known as Moyal equation
Density_matrix
Greek figurines made of terracotta
Psi, phi and tau were types of terracotta figurines made in Mycenaean Greece during the Late Helladic period. They were typically about 10 to 20 centimetres
Psi, phi and tau type figurine
Psi,_phi_and_tau_type_figurine
Algorithm in computational quantum physics
quantum system. The basic building block is a generic wave function | Ψ ( a ) ⟩ {\displaystyle |\Psi (a)\rangle } depending on some parameters a {\displaystyle
Variational_Monte_Carlo
Class of statistical estimators
M-estimator of ψ-type T is defined through a measurable function ψ : X × Θ → R r {\displaystyle \psi :{\mathcal {X}}\times \Theta \rightarrow \mathbb {R}
M-estimator
Mathematical concept
_{-\infty }^{\infty }\varphi (t)\Psi (t)\,dt\end{aligned}}} where ρ runs over the non-trivial zeros of the zeta function p runs over positive primes m runs
Explicit formulae for L-functions
Explicit_formulae_for_L-functions
Loss of quantum coherence
in non-relativistic quantum mechanics by a wave function ψ ( x 1 , x 2 , … , x N ) {\displaystyle \psi (x_{1},x_{2},\dots ,x_{N})} , where each xi is a
Quantum_decoherence
Theorem bounding the growth rate of analytic functions
functions besides the exponential function. In general, a function Ψ ( t ) {\displaystyle \Psi (t)} is a comparison function if it has a series Ψ ( t ) = ∑
Nachbin's_theorem
Short "burst" or "envelope" of restricted wave action that travels as a unit
A gaussian 2D quantum wave function: ψ ( x , y , t ) = ψ ( x , t ) ψ ( y , t ) {\displaystyle \psi (x,y,t)=\psi (x,t)\psi (y,t)} ψ ( x , t ) = ( 2 a 2
Wave_packet
Probability distribution
{W}}(\mathbf {\Psi } ^{-1},\nu )} . Important identities have been derived for the inverse-Wishart distribution. The probability density function of the inverse
Inverse-Wishart_distribution
Model of an energy potential in quantum mechanics
here by an Ansatz for the wave function of the type Ψ ( x , y , z ) = ψ ( x ) ϕ ( y , z ) {\displaystyle \Psi (x,y,z)=\psi (x)\phi (y,z)\,\!} . Alternatively
Delta_potential
Notation for quantum states
|{\boldsymbol {A}}{\bigr )}|\psi \rangle =\langle \phi |{\bigl (}{\boldsymbol {A}}|\psi \rangle {\bigr )}\,,} (in other words, a function composition). This expression
Bra–ket_notation
K(z)=A\exp \left(\psi (-2,z)+{\frac {z^{2}-z}{2}}\right)} where K(z) is the K-function and A is the Glaisher constant. The balanced polygamma function can be expressed
Balanced_polygamma_function
Second-order partial differential equation
{\displaystyle \psi _{x}=-v,\quad \psi _{y}=u,} and the irrotationality condition implies that ψ satisfies the Laplace equation. The harmonic function φ that is
Laplace's_equation
Principle of quantum mechanics
wave equation can be solved using functions of position, Ψ ( r → ) {\displaystyle \Psi ({\vec {r}})} , or using functions of momentum, Φ ( p → ) {\displaystyle
Quantum_superposition
Function that interpolates the factorial
− 1 , 1 , − x ) Γ ( − x ) {\displaystyle H(x)={\frac {\psi \left(1-{\frac {x}{2}}\right)-\psi \left({\frac {1}{2}}-{\frac {x}{2}}\right)}{2\Gamma (1-x)}}={\frac
Pseudogamma_function
Mathematical model in quantum mechanics
and energy) may all be derived from the wave function. The wave function ψ ( x , t ) {\displaystyle \psi (x,t)} can be found by solving the Schrödinger
Particle_in_a_box
Probability density function
Radiative Decays of the J/Psi and Psi-Prime, Ph.D. Thesis, SLAC-R-255 (1982). (This is a 205-page document in .pdf form – the function is defined on p. 178
Crystal_Ball_function
Quantum mechanics concept
3 = H e − α x {\displaystyle \psi _{3}=He^{-\alpha x}} Next, we know that the overall ψ {\displaystyle \psi } function must be continuous and differentiable
Finite_potential_well
Relativistic quantum mechanical wave equation
mechanics, the Dirac spinor ψ ( x ) {\displaystyle \psi (x)} corresponds to a four-component spinor wave function describing the state of a Dirac fermion. Its
Dirac_equation
International historically Black fraternity
Kappa Alpha Psi Fraternity, Inc. (ΚΑΨ) is a historically African American fraternity. Since the fraternity's founding on January 5, 1911, at Indiana University
Kappa_Alpha_Psi
( g ) ¯ , {\displaystyle \langle \phi ,\psi \rangle ={\frac {1}{|G|}}\sum _{g\in G}\phi (g){\overline {\psi (g)}},} where |G| denotes the order of G
Class_function
Family of solutions to related differential equations
}(\psi (k+1)+\psi (n+k+1)){\frac {\left(-{\frac {z^{2}}{4}}\right)^{k}}{k!(n+k)!}}} where ψ ( z ) {\displaystyle \psi (z)} is the digamma function, the
Bessel_function
Formulation of the quantum many-body problem
_{1}\psi _{2}+\psi _{1}\psi _{2}\psi _{1})+{\frac {1}{\sqrt {3}}}(\psi _{1}\psi _{2}\psi _{1}+\psi _{2}\psi _{1}\psi _{1}+\psi _{2}\psi _{1}\psi _{1})\right)\\=&{\frac
Second_quantization
)\int _{0}^{1}{\frac {\Psi (\mu ')}{\mu +\mu '}}H(\mu ')\,d\mu '} where the characteristic function Ψ ( μ ) {\displaystyle \Psi (\mu )} is an even polynomial
Chandrasekhar's_H-function
Generating function in integrable systems
}\psi _{j}\psi _{j+i}^{\dagger },\quad i=1,2\dots } are the ""current"" components. As seen in equation (9), every KP τ {\displaystyle \tau } -function
Tau function (integrable systems)
Tau_function_(integrable_systems)
Equation for fixed point of functional composition
given the function h, find the function Ψ such that ∀ x Ψ ( h ( x ) ) = s Ψ ( x ) . {\displaystyle \forall x\;\;\;\Psi {\big (}h(x){\big )}=s\Psi (x).} Schröder's
Schröder's_equation
Wavelet constructed using a spline function
integer m, the function ψ m ( x ) {\displaystyle \psi _{m}(x)} defined by ψ I , m ( x ) = d m d x m L 2 m ( 2 x − 1 ) {\displaystyle \psi _{I,m}(x)={\frac
Spline_wavelet
First known wavelet basis
wavelet function ψ ( t ) {\displaystyle \psi (t)} can be described as ψ ( t ) = { 1 0 ≤ t < 1 2 , − 1 1 2 ≤ t < 1 , 0 otherwise. {\displaystyle \psi
Haar_wavelet
{\partial \Psi (x,t)}{\partial t}}=H\Psi (x,t),} where we have to keep in mind that H {\displaystyle H} is an operator, not a simple number or function. There
Diffusion_Monte_Carlo
Evaluation of a function on its argument
In mathematics, function application (or evaluation) is the act of taking a function and an input from its domain to obtain the corresponding value from
Function_application
Multivariate generalization of the gamma function
the multivariate digamma function as ψ p ( a ) = ∂ log Γ p ( a ) ∂ a = ∑ i = 1 p ψ ( a + ( 1 − i ) / 2 ) , {\displaystyle \psi _{p}(a)={\frac {\partial
Multivariate_gamma_function
Marvel Comics fictional character
with his teenage counterpart, Psi-Lord, who had been raised by Nathaniel in a dimension outside of time. Franklin, as Psi-Lord, founds the team Fantastic
Franklin_Richards_(character)
Quantum mechanics principle
y , y ⟩ . {\displaystyle \langle \psi |x,x\rangle +\langle \psi |x,y\rangle +\langle \psi |y,x\rangle +\langle \psi |y,y\rangle .} The first and last
Pauli_exclusion_principle
Inverse of the gamma function
{1}{z^{4}}}\right)\,,} where ψ ( n ) ( x ) {\displaystyle \psi ^{(n)}(x)} is the polygamma function. This can be rigorously justified by the Lagrange inversion
Inverse_gamma_function
Probability distribution
\ln(X_{j})]=\psi '(\alpha _{i})\delta _{ij}-\psi '(\alpha _{0})} where ψ {\displaystyle \psi } is the digamma function, ψ ′ {\displaystyle \psi '} is the
Dirichlet_distribution
German mathematician (1831–1916)
Dedekind domain Dedekind eta function Dedekind-infinite set Dedekind number Dedekind psi function Dedekind sum Dedekind zeta function Ideal (ring theory) "Dedekind"
Richard_Dedekind
Extension of the factorial function
1 ) ( x ) > 0 {\displaystyle \psi ^{(1)}(x)>0} , where ψ ( 1 ) {\displaystyle \psi ^{(1)}} is the polygamma function of order 1. To prove the logarithmic
Gamma_function
Quantum mechanical phenomenon
quantitative effect. The wave function is expressed as the exponential of a function: Ψ ( x ) = e Φ ( x ) , {\displaystyle \Psi (x)=e^{\Phi (x)},} where Φ
Quantum_tunnelling
Divergent sum of positive unit fractions
digamma function is defined as the logarithmic derivative of the gamma function ψ ( x ) = d d x ln ( Γ ( x ) ) = Γ ′ ( x ) Γ ( x ) . {\displaystyle \psi (x)={\frac
Harmonic_series_(mathematics)
Mathematical function used to approximate atomic orbitals in quantum chemistry
\mathbf {E} _{1s}={\frac {\langle \psi _{1s}|\mathbf {\hat {H}} _{e}|\psi _{1s}\rangle }{\langle \psi _{1s}|\psi _{1s}\rangle }}} , where ⟨ ψ 1 s | ψ
1s_Slater-type_function
Computational statistics technique
cumulant-generating function as ψ θ ( η ) = ψ ( θ + η ) − ψ ( θ ) = ( μ + θ σ 2 ) η + σ 2 η 2 2 {\textstyle \psi _{\theta }(\eta )=\psi (\theta +\eta )-\psi (\theta
Rejection_sampling
Probability distribution
0 + i γ {\displaystyle \psi =x_{0}+i\gamma } f ( x ; ψ ) = 1 π Im ( 1 x − ψ ) = 1 π Re ( − i x − ψ ) {\displaystyle f(x;\psi )={\frac {1}{\pi }}\,{\textrm
Cauchy_distribution
Complex number whose squared absolute value is a probability
wave function ψ {\displaystyle \psi } belonging to the L2 space of (equivalence classes of) square integrable functions, i.e., ψ {\displaystyle \psi } belongs
Probability_amplitude
Function that can be used to build the wave function of a multi-fermionic system
antisymmetric wave function can be mathematically described as follows: Ψ ( x 1 , x 2 ) = − Ψ ( x 2 , x 1 ) . {\displaystyle \Psi (\mathbf {x} _{1},\mathbf
Slater_determinant
Mathematical function
u ) {\displaystyle \rho (u)} . This function is used to estimate a function Ψ ( x , y , z ) {\displaystyle \Psi (x,y,z)} similar to de Bruijn's, but
Dickman_function
Quantum mechanical model
in the coordinate basis, for the wave function ⟨ x | ψ ⟩ = ψ ( x ) {\displaystyle \langle x|\psi \rangle =\psi (x)} , using a spectral method. It turns
Quantum_harmonic_oscillator
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PSI FUNCTION