What is Notation: Definition and 1000 Discussions

In linguistics and semiotics, a notation is a system of graphics or symbols, characters and abbreviated expressions, used (for example) in artistic and scientific disciplines to represent technical facts and quantities by convention. Therefore, a notation is a collection of related symbols that are each given an arbitrary meaning, created to facilitate structured communication within a domain knowledge or field of study.
Standard notations refer to general agreements in the way things are written or denoted. The term is generally used in technical and scientific areas of study like mathematics, physics, chemistry and biology, but can also be seen in areas like business, economics and music.

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  1. Z

    Resistors, parallel line notation?

    I was looking at an answer regarding resistors, and saw the notation; R = R1 + R// where 1/R// = 1/R2 + 1/R3 I was wondering what the two parallel lines after the R indicate? Thanks.
  2. S

    Quantum optics - dirac notation

    Homework Statement http://quantum.leeds.ac.uk/~almut/section2.pdf Please note i am referring to the above notes I basically don't get how the maths works to get (eq(25))(eq(22))(eq(24)) = eq(26) am i missing something interms of the commutator relations ? Homework Equations The Attempt at a...
  3. S

    When to use Order Notation? (Error in Finite differences)

    Homework Statement I'm having a hard time understanding when we approximate higher order powers by order notation, especially when it comes to working out the Truncation Error for Finite Differences. My notes say "We use the order notation O(h^{n}) and write X(h) = O(h^{n}) if there exists a...
  4. L

    Angular momentum quantum numbers and spectroscopic notation

    Homework Statement find each of the angular momentum quantum numbers and the spectroscopic notation of the ground state electron configuration. Homework Equations n2s+1L J The Attempt at a Solution so for "each of the angular momentum quantum numbers" I am just finding the L in...
  5. N

    Learning Dirac Notation: Writing Hamiltonian for 3 States

    I am new to quantum physics. My question is how to write the Hamiltonian in dirac notation for 3 different states say a , b , c having same energy. I started with Eigenvaluee problem H|Psi> = E|psi> H = ? for state a? SO it means that indvdually H= E (|a><a|) for state a and for all three...
  6. C

    Evaluating a term in bra-ket notation

    Hi, i am evaluating the integral \int_{-\infty}^{+\infty}dE \langle p'|E \rangle \langle E| e^{-iEt/ \hbar} |p\rangle However, i am unsure how to evaluate \langle E| e^{-iEt/ \hbar} |p\rangle . I am not sure if it is simply e^{-iEt/ \hbar} \times \langle E|p\rangle or something else. Any...
  7. nukeman

    Vector Notation with force and displacement help. Thanks

    Homework Statement This is not a homework question, but rather a review question. I have the answer, ill post below, but have no idea how to get to the answer :) Question: "A constant force of 90.0N acts on a ball while it has a displacement of 1.40m at 10 degrees below the x-axis. The...
  8. I

    Summing Series (Sigma Notation)

    Homework Statement a) nƩr2(r-1)r=1 Homework Equations Using the summation series formulae... The Attempt at a Solution So far I have got: r2(r-1) = r3-r2 Ʃr3 = \frac{1}{4}n2 (n+1)2 Ʃr2 = \frac{1}{6}n(n+1)(2n+1) Therefore, Ʃr3-r2 = \frac{1}{4}n2 (n+1)2 -...
  9. T

    What Do Upper and Lower Indices in Tensor Notation Signify?

    Hi, I am very new to general relativity and have only just started to learn how to do some very basic manipulation of tensors. I can understand the methods I am using and have some idea of what a tensor is but am not sure what the difference between upper and lower indices signifies. I can...
  10. A

    Notation for Weak Nuclear Force Particles

    The notations are: W^+, W^-, and Z^0. I'm assuming the W stands for Weak. But, why Z for the neutral one? Is there even a reason?
  11. M

    Can someone with this notation? vectors

    Homework Statement I'm sure this is quite simple, but I don't understand the notation. This is from a supplemental book that we have to do outside of class--there isn't a matching textbook and I really don't understand what they want here. Homework Equations I noticed that if i square...
  12. V

    Wavefunction in Dirac notation

    Homework Statement For the infinite square well, a particle is in a state given by \psi = \frac{1}{\sqrt 2}(\psi_1 + \psi_3) , where \psi_1 and \psi_3 are energy eigenstates (ground state and the second excited state, respectively). Represent this state as a column matrix \psi> in...
  13. K

    Calculate Expectation Value of Hamiltonian using Dirac Notation?

    Homework Statement I have the state: |\psi>=cos(\theta)|0>+sin(\theta)|1> where \theta is an arbitrary real number and |\psi> is normalized. And |0> and |1> refer to the ground state and first excited state of the harmonic oscillator. Calculate the expectation value of the Hamiltonian...
  14. I

    What is the significance of square brackets in tensor notation?

    What is meant by things like: R_{[abc]} and also things like: \nabla_{[a\nabla_b]} Where you have square brackets in the subscript? Thx
  15. E

    Understanding Set Notation: Exploring the Relationship Between Sets S and W

    Ok, I'm not very familiar with set notation. I was just wondering if the following is correct notation and means what I think: {x\inS : \existsy\inx, y\inW} S is a set of pairs of symbols (tuples of length 2 is the technical term I believe). W is a set of symbols. What I want is the...
  16. L

    Predicate logic and one point rule using Z notation

    Hello all, I'm in the process of simplifying the following equation using one-point rule and other predicate logic. But I’m a bit stuck with where to start or which inference rule to use first. Please help or any pointers would be much appreciated. Thanks
  17. B

    Function notation minus one exponent?

    Hi ! What does the notation mean exactly when a function has power minus one ? For example i have seen the logistic function written as: f(x) = f0[1 + exp(−βx)]^-1
  18. R

    Having trouble understaning the notation co-variances

    Can someone explain to me how Cov(x,y)=[X-E(x))(Y-E(y)] and this would equal 0 under the normal OLS assumption. I know how to calculate the covariance, but X here is a matrix. So I don't understand the logic of this formula...
  19. L

    Calculate J Notation Impedance of Network w/ Capacitor & Inductor

    Homework Statement We have a capacitor in parallel with an inductor. These are both in series with a resistor and capacitor. Calculate the J notation Impedance of the network. I only want the initial basic solution. The problem I have is that sometimes the J notation of C is -ve and...
  20. N

    Dirac Notation and Magnitude of Bra's Help

    Hi all, I was diving into my 3rd year quantum assignment and I saw the following which I have to use for the rest of the question to prove the Cauchy-Schwarz inequality: Homework Statement || a|x> + b|y> ||^2 I only really learned a bit about Dirac notation last year, so please...
  21. D

    Big O Notation: Better Approximation than o

    While discussing Taylor's theorem, my professor pointed out that for n=2, Taylor's Theorem says: f(x) = f(x_{0}) + f'(x_{0})(x - x_{0}) + O(|x - x_{0}|^{2}) He then emphasized that O(|x - x_{0}|^{2}) is a much better approximation than o(|x - x_{0}|). But how is O(|x - x_{0}|^{2}) a...
  22. A

    What do these molecular term symbols mean?

    I'm trying to decipher exactly what it means to say the following things: (1) The ground electronic state of NO_2 is ^{2}A_1; (2) The ground electronic state of ClO_2 is ^{2}B_1; (3) The ground electronic state of O_2 is ^{3}\Sigma^{-}_g. I really don't have a clue what these symbols...
  23. D

    Is y'(x) a Valid Notation for a Derivative Function?

    This is just me being pedantic :)
  24. J

    Very quick question about vector notation

    Homework Statement http://people.math.carleton.ca/~mezo/A5math1102-11.pdf number one Homework Equations The Attempt at a Solution What does Z5/5 mean?
  25. U

    Normalised Energy Eigenfunction (Probability with Dirac Notation)

    Homework Statement Normalised energy eigenfunction for ground state of a harmonic oscillator in one dimension is: 〈x|n〉=α^(1/2)/π^(1/4) exp(-□(1/2) α^2 x^2) n = 0 α^2=mω/h suppose now that the oscillator is prepared in the state: 〈x|ψ〉=σ^(1/2)/π^(1/4) exp(-(1/2) σ^2 x^2)...
  26. S

    I'm trying to figure out what the summation notation of

    I'm trying to figure out what the summation notation of (1-x1)^θ * (1-x2)^θ * ...(1-xn)^θ would be for summation I know I need to convert this to a summation notation in order to solve my problem, but I can't figure out how to convert it. Any help will be appreciated.
  27. K

    Prime Number Related Notation Question

    Is there any standard (or reasonably standard) notation for the following function? Basically, it's ∏(n) - ∏(n-1) or, which is the same thing, \frac{\Lambda(n)}{\log n} (where ∏(n) is the Riemann prime counting function and \Lambda(n) is the Von Mangoldt function) Basically...
  28. O

    Help with Vector Notation: \partial_{\mu} \phi^{*}\partial^{\mu} \phi

    Not a particularly direct question, just something I don't mathematically understand and would very much appreciate help with. For some scalar field \phi, what would \partial_{\mu} \phi^{*}\partial^{\mu} \phi mean in mathematical terms. ie how would I calculate it? From what I understand...
  29. S

    Help with tensor notation and curl

    Homework Statement Show that \nabla \times (a \cdot \nabla a) = a\cdot\nabla(\nabla\times a) + (\nabla \cdot a(\nabla \times a) - (\nabla \times a)\cdot \nabla aHomework Equations \nabla \times (\nabla \phi) = 0 \nabla \cdot (\nabla \times a) = 0 The Attempt at a Solution I started with...
  30. G

    What does this notation mean?

    If you look here http://planetmath.org/encyclopedia/RiezsLemma.html , there seems to be something missing - nothing is said about the norm of (x_alpha) or about the norm of (s - x_alpha). Now, the same thing seems to happen here...
  31. S

    F=ma, kinematics in vector notation

    I'd like to go over my approach to a question I am doing right now, but I've posted my general approach instead of the question itself. Say there is some object with three forces acting on it, and these forces are given to me in vector notation (i.e. with unit vectors "i" and "j"). I am also...
  32. A

    Dirac Notation - Position and Momentum

    Homework Statement Show that \left\langlex|p|x'\right\rangle = \hbar/i \partial/\partialx \delta(x-x') 2. The attempt at a solution \left\langlex|p|x'\right\rangle = i\hbar \delta(x-x')/(x-x') = i\hbar \partial/\partialx' \delta(x-x') = \hbar/i \partial/\partialx \delta(x-x') For...
  33. P

    Simple index notation question

    Is Tab\partialcf = Tac\partialbf, where T is a tensor? Seems to me like you should be able to do this: Tab\partialcf =Tab\deltabc\partialbf =Tac\partialbf Maybe I'm using the Kronecker delta incorrectly. Could someone check this for me?
  34. A

    Angular momentum in bracket notation

    Hello, why is <j' m' | j m>=0 if j \not= j' \; \text{or} \; m \not= m' j and m are describing states. I don't understand why an 'empty bracket' behaves like that.
  35. I

    Meaning of Derivative Notation in Denominator

    What is the meaning of \frac{\partial F(x)}{\partial(\partial f(x)/\partial x)} in which a derivative appears in place of the variable x in the denominator? Anyone, please?
  36. S

    Notation Convention: Primes in Coordinate Transformations

    I have seen in various locations different conventions regarding the location of a prime symbol denoting a tensor represented in a new frame. For example, if the position four-vector is x^{\mu} then this four-vector in a different frame is often written as either x'^{\mu} or...
  37. T

    Confused about notation for computing gradients

    Homework Statement Consider scalar functions u = u(x). Compute the gradients ∇u for: u(x) = (x, y, z) u(x) = (y, z, x) u(x) = (x^2y, 10, z + x) Homework Equations This is a question on my homework for undergraduate Fluid Mechanics. The teacher has been assigning math problems in topics...
  38. D

    Partial Differentiation with Einstein Notation

    Hi there, I'm writing a research paper and have hit a roadblock, (wikipedia did not help) and one of my collaborators sent me an e-mail that I do not understand. I am attempting to find when the following functional is stationary: T = \int\limits_{\lambda_{1}}^{\lambda_{2}}...
  39. C

    Determining Time Difference for Two Free-Falling Diamonds at a Given Distance

    Homework Statement Two diamonds begin a free fall from rest from the same height, a time "delta t" apart. How long after the first diamond begins to fall will the two diamonds be a distance "d" apart? Give your answer in terms of the variables given and "g". ( Solve for t= ) Homework...
  40. T

    How do I choose the correct angle when graphing vectors from unit notation?

    Homework Statement Draw the following vector. Label the angle that specifies the vector's direction, then find its magnitude and direction. Homework Equations vector a = 2.0i - 6.0j The Attempt at a Solution I get stuck here: I don't know which angle to use.
  41. A

    Very Basic questions on bra-ket notation

    Hello, i am a beginner in quantum mechanics and i have those basic questions on the bra-ket notation: Which dimension has a ket | \phi > describing a state normally? Maybe \quad C ^n? Which dimension has a bra-ket <\psi | \phi >then? Maybe \quad C ? How do you get the matrix...
  42. S

    Set builder notation and proofs

    "set builder" notation and proofs I'm curious about the references to "set builder" notation that I see in forum posts. Is this now a popular method of teaching elementary set theory and writing elementary proofs? I haven't looked at materials for that subject in the past 20 years. The...
  43. D

    Adding scientific notation question =)

    Homework Statement Add (9.8x10^3s)+(9.9x10^4s)+(0.017x10^6s) Homework Equations None The Attempt at a Solution I have entered 125800, as well as 1.26x10^5 but the website marked both of those wrong. I've done this problem every way you could do it I think and it comes out to the same answer...
  44. G

    Interval notation and specifying units (v vs. t graph)

    Homework Statement #5 and #6 of the attached pdf on page 5 (graph on page 4 relates to said problems) Note: The professor did not cover how to do a problem like this, and the book does not have a similar problem, nor any other handouts. This definitely was a unique question. I'm unsure if I...
  45. 1

    Unit Vector Notation Addition

    Homework Statement Consider the following vectors: a = (5.0m) i + (2.0m) j b = (-14m) i + (6.0m)j Sum of a+b in unit vector notation? Homework Equations The Attempt at a Solution I'm not sure about this notation, all I know about adding vectors is graphically. Does (5.0m)...
  46. A

    Question about a logic notation

    (x∈R → f(x)>0) → f is asmani. What does it mean: 1. If there exists some x in R such that f(x)>0, then f is asmani. 2. If for all x in R we have f(x)>0, then f is asmani. 3. It's ambiguous or meaningless. 4. ...? Thanks in advance.
  47. G

    Place following in scientific notation

    Homework Statement Place the following in scientific notation. T = 2pi. Homework Equations The Attempt at a Solution Would I just put 2pi into scientific notation?
  48. P

    Notation for Vectors in Different Bases

    What I usually mean by a vector, x, is a quantity which can be written (using Einstein summation convention) as xi ei = xi' ei' and so on. In other words the scalar components {xi} change according to the set of base vectors {ei} I choose. But occasionally, in the context of changing bases...
  49. V

    Is ln(x)3 the Same as [ln(x)]3? Decoding Logarithm Notation

    Homework Statement is ln(x)3 the same as saying [ln(x)]3? Also, if there is a difference, which one applies to the exponent being moved into the front of the logarithm as in 3ln(x)? Homework Equations natural logarithms The Attempt at a Solution I just got tripped up on the...
  50. R

    Help with sigma notation where the top value is x?

    Homework Statement In each case, x is an integer between -6 and 6 inclusive. Homework Equations x Σ 2i =12 i=1 The Attempt at a Solution 2x1 = 12 + 2x2 = 12 +...+2x(x) = 12
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