What is Derivation: Definition and 1000 Discussions

In cryptography, a key derivation function (KDF) is a cryptographic hash function that derives one or more secret keys from a secret value such as a main key, a password, or a passphrase using a pseudorandom function. KDFs can be used to stretch keys into longer keys or to obtain keys of a required format, such as converting a group element that is the result of a Diffie–Hellman key exchange into a symmetric key for use with AES. Keyed cryptographic hash functions are popular examples of pseudorandom functions used for key derivation.

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  1. E

    I Rotational-Vibrational Energy state equation derivation

    I am having a mental block at the moment and for some reason I can't seem to derive these two equations: From this equation: Any assistance would be much appreciated!
  2. G

    I Hartree fock derivation problem

    Can anyone show the algebra that leads to the rewriting that I have underlined in the attachment. It is a derivation It is taken from the start of a derivation of the roothans method of hartree fock from 1972 with the authors Snow and Bills.
  3. Enigma322

    I Q about Fourier Coefficient Derivation

    For the calculation of cn u have to multiply the equation ∑ cn * ejnx by e-jmx what is the reason for this? in my textbook it says nothing about it and on some sites it just said "without justification" i guess what I am asking is why does this do what we want? ps: how do u properly make...
  4. P

    I Relativistic Kinetic Energy Derivation

    Hello, I tried a different route to derive relativistic kinetic energy and I cannot see why it doesn't work. Here is my work: 8.00000000000000E+01 RM, Rest mass of object 7.50000000000000E+05 v, velocity of object 6.00001877636573E+07 Momentum, p,= RM/Sqrt(1-(v^2/c^2))*v...
  5. T

    Integration of Maxwell speed distribution function

    Homework Statement Show the steps needed to obtain the equation for average molecular speed, cavg=√8RT/πM from the integral (from negative infinity to infinity) ∫v*f(v)dv where f(v) is the Maxwell distribution of speeds function f(v)=4π*(M/2πRT)1.5v2e-Mv2/2RT M is the molar mass of the...
  6. S

    I Derivation of the photon energy

    Hi everyone, Anybody knows if the photon energy (frequency * Planck's constant) can be derived from more basic physical principles or this formula was "invented" to explain the photo-electric effect or black body radiation? If you know a way to derive it, please share. Thanks a lot !
  7. S

    I Can Anyone Help Understand Einstein's 1905 Derivation of E=mc^2?

    Link: https://www.fourmilab.ch/etexts/einstein/E_mc2/www/ The only part I'm having trouble with is how he gets the plus sign in that 1+(v/c)cos(φ) numerator for the "other" light ray (emitted in the opposite direction of the first). My understanding is that the φ he uses in his general Doppler...
  8. BobTheLawyer

    Derivation of Cholesky Decomposition

    Homework Statement Derive Cholesky Decomposition for a 3x3 matrix Homework Equations IN: S is Real matrix with dimensions 3x3 and is Symmetric and semi-definite Out: L is a Real matrix with dimensions 3x3 such that S=L*L^t L is lower-triangular The Attempt at a Solution We learned this in...
  9. V

    Derivation of Aerodynamic Forces

    Good day all: I'm having trouble deriving the forces for Lift and Drag in the attached diagram. The text I have (Fundamentals of Aerodynamics - John Anderson) states the solution to be: L = N cosα - A sinα D = N sinα + A cosα Can anyone guide me through this? I think the cofunction identity...
  10. Asleky

    Dynamics: Incline Slope Derivation Simplification

    Homework Statement No official problem, just a study guide fill-in-the-blanks with an extended simplification blank. Basically, no values were given, and it is a standard block on a standard slope with a north-east applied force pushing down on the block (not parallel to horizontal or vertical...
  11. H

    Simple derivation: sphere contracting under gravity

    Hi Guys, I'm reading Roger Penrose's book "The Road to Reality" at the moment and I wonder if you could help me out with a pretty simple derivation which he doesn't describe in complete detail. On page 399 he considers a sphere of mass contracting under gravity, and says "The rate of volume...
  12. W

    Derivation of the Christoffel symbol

    I'm reading Zee's Gravity book, can anyone help me understand the explanation on this part, I understand everything except the last part, he said to use (I.4.14) so that I could solve for the quantity shown in the image, what does he mean by that and how?
  13. Z

    Velocity Equation Derivation For Radiation Beaming

    Homework Statement [/B] Radiation beaming (cone) from an object traveling towards you at some velocity 'v' with the observed flux enhanced by an amplification factor 'a'. Derive an equation for the velocity 'v' needed to produce an amplification factor 'a'. Thank you Homework Equations...
  14. A

    Virial equation second coefficient derivation

    I've been stuck over this integral for around an hour while studying the derivation of the second coefficient of the virial equation: ∫∫dx1d x2 γ(x1,x2) where γ(x1,x2) is 1 when x1 - x2 < constant. = V∫ dx2 γ(x1,x2) where V is the integral of dx1. Given: periodic boundary condition: x1 + V = x1...
  15. F

    Derivation of the speed of sound waves equation

    I'm learning about the speed of sound waves through a medium. The derivation is initiated through Impulse=change in linear momentum (I=Δp), then I=ΣFΔt=(Area×Δpressure×Δt) in the x direction The derivation proceeds by replacing the Δpressure with another equation we had derived earlier...
  16. R

    What could be causing discrepancies in my derived formula for max. LOS range?

    I went through my Physics textbook where we have a chapter on Communication systems. There's a certain section where they show us the formula for the LOS max. range for a tower with a given height (say h) but I, unsatisfied with it, set out to derive it myself at home and wasn't convinced with...
  17. askhetan

    Understanding operators for Green's function derivation

    Dear All, I am trying to understand what operators actually mean when deriving the definition of green's function. Is this integral representation of an operator in the ##x-basis## correct ? ## D = <x|\int dx|D|x>## I am asking this because the identity operator for non-denumerable or...
  18. RedDelicious

    Relativistic Kinetic Energy Derivation

    Homework Statement This problem comes from an intermediate step in the textbook's derivation of relativistic energy. It states that E_k\:=\:\int _0^u\frac{d\left(\gamma mu\right)}{dt}dx then leaves the following intermediate calculation as an exercise to the reader: Show that...
  19. G

    Horizontal Tangents in the Graph of y = 3x + 6sinx

    Homework Statement Does the graph of the function y = 3x + 6sinx have any horizontal tangents in the interval 0 ≤ x ≤ 2 If so, where? Homework Equations Derivative rules The Attempt at a Solution I tried finding the derivative and setting it equal to zero. y' = 3 + 6(cosx) 3 + 6(cosx) = 0...
  20. heartshapedbox

    Taking the derivative of position to get velocity

    Homework Statement The problem is hopefully attached, I had to take a screen shot. Homework Equations I understand the process of taking the derivative of position to get velocity. *refer to derivative rules... for example r(x)=2x^2-6x+8 therefore r`(x)=4x-6 The Attempt at a Solution I am...
  21. Z

    Derivation of Wien's+Reyleigh-Jean's Laws from Planck's Law

    Homework Statement After reading the forum stickies I'm not entirely sure where to put this question since it involves using math to solve a question, but is informally stated and isn't a book problem, either-I just started reading Fong's Elementary Quantum Mechanics, and in the first few...
  22. B

    Snell's Law: Parallel Polarization Derivation

    Hi, I have a plane-wave incident upon a planar interface that is perpendicularly polarized with an electric field directed out of the page in the y-hat direction, perpendicular to the x-z plane of incidence. An image of the incident plane: I'm also given the general expressions for the...
  23. Gwyndolin

    How to derive formula for nucleus decay using this equation?

    Homework Statement The formula being derived is N=No*e^k*t, from the equation Nn=No/2^n where No is the initial number of particles and the lowercase n in the second equation is the number of half lives. The n in Nn just indicates the number of particles after so many half lives. You might also...
  24. jeszie

    Can you explain x=1/2(vi+vf)t?

    Can you explain, or prove why we have this equation as I'm interested in learning the equation as well as knowing from where that people derive it? Thanks
  25. Y

    Derivation of Mutual Inductance Energy

    I've attached a picture of my book. So there is a figure of two inductors mutually connected. The book says that initially, current 1 and current 2 are zero. Then when current 1 goes from 0 to I1, the energy stored in circuit is only the energy in inductor 1. <-- This is my question, but...
  26. teroenza

    Breit-Rabi Formula Derivation for j=1/2

    Homework Statement Derive the Breit-Rabi equation in the case that the quantum number j is equal to 1/2, specifically the 1S_1/2 state of Hydrogen. This is the equation describing hyper-fine and Zeeman splitting of the energy levels in an applied magnetic field. Homework Equations We are given...
  27. T

    Finite geometric series formula derivation? why r*S?

    what is the rationale of multiplying "r" to the second line of series? why does cancelling those terms give us a VALID, sound, logical answer? please help. here's a video of the procedure
  28. K

    Magnetic dipole moment derivation

    (2) Hi. I am having a problem with understanding how to approximate 1/R in the forms of equations written above. I took this equations from a blog, and it tells that I can use talyor polynomial. but I don't get there somehow.
  29. T

    Derivation for curl of a vector

    I have attached the equation that I do not quite understand how is true. This is the current density and was simply used as a part of a proof. But how is this equation true? How does taking the curl of J give you this expression?
  30. D

    Goldstein Derivation 1.6: Nonholonomic Constraints in Particle Motion

    1. The problem statement A particle moves in the ##xy## plane under the constraint that its velocity vector is always directed towards a point on the ##x## axis whose abscissa is some given function of time ##f(t)##. Show that for ##f(t)## differentiable but otherwise arbitrary, the constraint...
  31. T

    Deriving B.31 in PDF on Squared-Angular Momentum

    I was looking at this PDF (http://www.ifi.unicamp.br/~maplima/fi001/2012/aula20b.pdf) showing the derivation of the squared-angular momentum operator. Everything seems okay although I am just slightly lost in how exactly B.31 was derived. Isn't B.31 equal to the dot product of B.24 with itself...
  32. K

    Coulomb gauge derivation (static field)

    Hi, I am a little confused of derivation of Coulomb Gauage. (2) First, prime notation is adopted to describe the magnetic field density source current. Non-prime notation is for position that we are specifically interested in (ex. the position magnetic force acts on)...
  33. A

    LSZ reduction formula derivation following Peskin's book.

    Question: In page number 225 of Introduction to quantum field theory of peskin and schroeder, looking at the equation that follows to Eq. (7.41), I cannot understand how the general state $|\lambda_K>$ (one eigenstate of the full Hamiltonian Lorentz shifted so its momentum be K) is annihilated...
  34. A

    Derivation of Rutherford Scattering - angular momentum

    Homework Statement I am trying to show that as the alpha particle is being scattered, the angular momentum magnitude at point M is m r^2 \frac{d \phi}{dt}. Diagram: Homework Equations Linear Momentum: ##\vec L = \vec r \times \vec p ## Repulsive Coulomb Force: ##\vec F = \frac{k 2Ze^2}{r^2}...
  35. F

    How to find the charge density given by a Tricky Potential?

    Homework Statement I am trying to solve Problem 2.45 in Electrodynamics by Griffiths, however, my answers were different from those in the book, I am suspect I got a missing step but I could not find it, so here is the Given Problem Find the charge density \rho given by a potential...
  36. Alain De Vos

    Line element and derivation of lagrange equation

    With coordinates q en basis e ,textbooks use as line element : ds=∑ ei*dqi But ei is a function of place, as one can see in deriving formulas for covariant derivative. Why don't they use as line element the correct: ds=∑ (ei*dqi+dei*qi) Same question in deriving covariant derivative,
  37. T

    Derivation of Minkowski norm of the four-momentum

    I have attached a derivation of the Minkowski norm of the four-momentum but just don't quite see how the writer arrived at ## -m^2 c^2 ## from what was given. How exactly does this quantity follow from ## -\frac {E^2}{c^2} + p^2##? I feel like it might be very obvious, so any explanation would...
  38. bananabandana

    Euler Lagrange Derivation (Taylor Series)

    Mod note: Moved from Homework section 1. Homework Statement Understand most of the derivation of the E-L just fine, but am confused about the fact that we can somehow Taylor expand ##L## in this way: $$ L\bigg[ y+\alpha\eta(x),y'+\alpha \eta^{'}(x),x\bigg] = L \bigg[ y, y',x\bigg] +...
  39. T

    Derivation of number of quantum states

    Hi, I recently saw a derivation that included: [1] #CS = V_spatial * V_momentum [2] #QS = #CS/h (where # indicates it's the total number of the variable) quantum states = QS; classical states = CS; h is Planck's constant If possible, do you mind explaining or directing me to references...
  40. DuckAmuck

    Sloppy Derivation of Euler-Lagrange.

    Just wondering how much validity there is to this derivation, or if it's just a convenient coincidence that this works. We have a Lagrangian dependent on position and velocity: \mathcal{L} (x, \dot{x}) Let's say now that we've perturbed the system a bit so we now have: \mathcal{L} (x +...
  41. avikarto

    Deriving J=L+S from General Expression: Tips & Tricks

    I am trying to derive that ##\vec{J}=\vec{L}+\vec{S}## (in free space) starting from the general expression ##\vec{J}=\int dV\epsilon_0\: \vec{r}\times\left(\vec{E}\times \vec{B}\right)##. I get to the point where I have that ##\vec{J}=\epsilon_0\int dV...
  42. H

    Propagator in the derivation of path integrals

    Why isn't (5.298) the following instead? ##K(x, t_1; x', t_0) = \delta(x-x')\,e^{-\frac{i}{\hbar}H(t_1-t_0)}## My reasoning: Since \Psi(x, t_1) = e^{-\frac{i}{\hbar}H(t_1-t_0)}\,\Psi(x, t_0)\\ = e^{-\frac{i}{\hbar}H(t_1-t_0)}\,\int\delta(x-x')\Psi(x', t_0)\,dx' The exponential operator with...
  43. S

    Fourier transformation and test function -- Question in the derivation

    How does it work? (The derivative rules of FT) We look at $$F[x(t)]=\hat{x}(f)$$ $$\mathcal{l} \text{ is a distribution, with}\tilde{x}=tx(t)$$ $$\mathcal{F}[Dl(x)]=\mathcal{F}l'(x)=2\pi il(\mathcal{F}\tilde{x})=2\pi i \mathcal{F}l(\tilde{x})$$ Till here I fully understand. But next step...
  44. F

    What is the electric field due to hollow sphere at R=z?

    So I derived the E-field of a hollow sphere with a surface charge σ at z and I got: E(r)=\hat{z}\frac{\sigma R^2}{2\varepsilon _{0}z^2}\left ( \frac{R+z}{\left | R+z \right |}-\frac{R-z}{\left | R-z \right |} \right ) at z>R, the equation becomes: E(r)=\hat{z}\frac{\sigma R^2}{\varepsilon...
  45. davidbenari

    Why does Bohr's derivation work?

    Bohr assumed angular momentum was quantized as ##L=n\hbar##. But really it is quantized as ##L=\hbar \sqrt{l(l+1)}##. What he does to derive,e.g., the Bohr radius is consider that the total energy of an electron orbiting a proton is ## E=\frac{L^2}{2mr^2}-\frac{k e^2}{r} ## and then he makes...
  46. rosaliexi

    Derivation Constants/Rate of Change

    Hi, I'm working on a process control question about a tank system at steady state. The part I'm having problems with is where I have derived a second order differential equation to model the system and have replaced the concentrations with derivation constants in that : Actual Concentration at...
  47. H

    Why Is Bloch's Theorem Derived Using Complex Methods?

    Why are the solutions satisfying ##\psi(x+l)=\lambda\,\psi(x)## (4.191) the only physically admissible solutions? (##l## is the period of the periodic potential.) We may argue that the probability of finding an electron at ##x##, ##|\psi(x)|^2##, must be the same at any indistinguishable...
  48. J

    Derivation of moment of inertia of a solid sphere

    Homework Statement I need to know why my derivation does not work. I am attempting to derive I=2/5 mR^2Homework Equations I have seen people derive it using disks but my question is why do the shells not work? Where in my set up did I go wrong? Thanks The Attempt at a Solution I am attempting...
  49. I

    Graphical Derivation of x = Asin(ωt)

    Homework Statement Deriving the equation for simple harmonic motion, x = Asinωt, graphically. Homework Equations ω = 2πf, where f = 1/T 2. The attempt at a solution Take a sine curve as the simple harmonic motion (displacement, x, on y-axis; time, t, on x-axis), then transform it. The...
  50. M

    Derivation of wave equation using tension of a string

    Homework Statement I'm currently following the textbook Advanced Engineering Mathematics by Erwin Kreyszig. I'm learning the derivation of the Wave equation using the method shown in the book, but when I reached the final part of the derivation, the working just confuses me. (1/Δx)[ (u/dx)|...
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