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. WannabeNewton

    Quick question, Komar integral derivation in Wald

    I'm trying to follow Wald's derivation of the Komar mass on page 288. We start with an asymptotically flat static space-time with killing vector ##\xi^{a}##. Let ##\Sigma## be a hypersurface orthogonal to ##\xi^{a}## and let ##S\subseteq \Sigma## be a topological 2-sphere. The quantity ##F =...
  2. L

    Derivation of Planck's constant

    Homework Statement In a textbook I have, What is Quantum Mechanics?-A Physics Adventure, second edition,1996, Page 54, states that h=kβ, where h is Planck's constant; k is Boltzmann's constant, and β is Wien's constant. I have multiplied Boltzmann's constant times Wien's constant, but it does...
  3. L

    Question about Geodesic Equation Derivation using Lagrangian

    I'm trying to derive the Geodesic equation, \ddot{x}^{α} + {Γ}^{α}_{βγ} \dot{x}^{β} \dot{x}^{γ} = 0. However, when I take the Lagrangian to be {L} = {g}_{γβ} \dot{x}^{γ} \dot{x}^{β}, and I'm taking \frac{\partial {L}}{\partial \dot{x}^{α}}, I don't understand why the partial derivative of...
  4. K

    Derivation of Spin-orbit Coupling

    I was reading Griffiths's book on quantum mechanics. In chapter 6, he tried to derive the spin-orbit coupling using a classical approach. H=-\vec{\mu}\cdot \vec{B} 1. Finding the relation between \vec{μ} and \vec{S} He consider a spinning charged ring with mass m, radius r, total charge...
  5. H

    TRIGONOMETRY equation derivation [HELP]

    The signal length from satellite to the Earth station (AC) can be found as 2(H)/[{sin^2(theta)+(2(H)/R)}^1/2+sin(theta)] Due to the Earth projection where "H" is satellite height and and R is the Earth radius My question is Can you help me to derive this equation? how they have...
  6. C

    Counterterms Feynman Rules Derivation

    Does anyone have a link or a reference to somewhere where these rules are explicitly derived for phi-four theory?
  7. C

    Equipotential Field line equation derivation

    Hello, This is not a homework question! I am simply trying to understand for my own amusement. A while back I synched Solidworks and Excel, and am using this to create 3d models of different things such as dipoles for visual interpretation. So in doing this I needed to find potential...
  8. T

    Help me understand this derivation for hall voltage?

    Derivation: http://s24.postimg.org/nhiqgg4qt/untitled.png How did they get ΔV=Ed? (d=width of the conductor) Sorry, I'm really rusty on my physics. Finding it quite difficult to review.
  9. BruceW

    Quantum Operator Derivation: Exploring Intuitive Approaches

    Hi all! I was reviewing some basic quantum mechanics, and I was trying to 'derive' the equation -i \hbar \frac{\partial}{\partial x} \psi_{(t,x)} = <x| \hat{P} | \psi > using the commutator relation, and the form of the identity operator. OK, I know that the proper, mathematical way to prove the...
  10. K

    Torricelli's theorem Derivation help

    Homework Statement In torricellis theorem why we take P1=p2=atmospheric pressure? Homework Equations The Attempt at a Solution
  11. M

    Need help understanding this thermo. derivation

    Im trying to understand this concept of deriving an expression for (\frac{\partial T}{\partial P})s in terms of T, V, Cp, \alpha, and \kappaT (\frac{\partial T}{\partial P})s is evaluated by measuring the temperature change and the specific volume change accompanying a small pressure change...
  12. K

    Bernoulli Equation Simple derivation help

    Homework Statement Please help me as I am quite confused in Bernoulli's theorem derivation...In my textbook,it is considered that Fluid Moves from a Greater height h1 to lower height h2,The pressure on upper end is positive,while at the lower end,it is negative,i.e against the motion of...
  13. ash64449

    Derivation of lorentz transformation

    Hello friend, I want to know how to derive lorentz transformation. Even though i have book that derived lorentz transform,i am not able to understand. I hope you give me an easy derivation of it!
  14. K

    How Is Acceleration Derived in a Frictional System with Two Boxes?

    Two boxes are side by side on a floor with friction, from the left a Force acts on them. To be more concise about the picture it is this one on this website: http://hyperphysics.phy-astr.gsu.edu/hbase/f2m2.html#c1 I don't understand how the acceleration is derived. Especially i don't get...
  15. A

    Equation - Wave Equation Derivation Question

    equation -- Wave Equation Derivation Question Hello, my teacher says that if, on a wave equation f(x-ct)=f(e) then \partial_{ee}= \partial_{tt}- c^2 \partial_{xx} but i think that \partial_{t}=\frac{\partial }{\partial e} \frac{\partial e}{\partial t}=-c\frac{\partial }{\partial e} and...
  16. Sunil Simha

    I need to understand this derivation on solubility

    Homework Statement This is a derivation of the relation between solubility of a salt and pH of the solution in which it is dissolved from our textbook. Consider a salt MX whose Ksp=[M+][K-] If this were dissolved in a solution of the acid HX whose Ka=[H+][X-]/[HX] then what would be its...
  17. C

    Is Conservation of Energy Sufficient for Deriving the Adiabatic Process?

    Most of the book using PV=nRT for PV^gamma constant for adiabatic process. However, please refer attachment, proving using conservation of energy will also make sense?
  18. U

    Air resistance equation derivation

    I would like to derive the air resistance equation showed in the attached photo. A little while ago, I tried asking at a different forum, however, the users were very experienced and omitted several stages of the derivation, and thereby made the interpretation difficult as I am new to math, but...
  19. B

    Quantum mechanical derivation of Einstein's equations

    This result will shortly revolutionize physics. This short paper breaks the barrier which has kept time as a C-number in the quantum theory while the other spacetime dimensions are operators. Amazing! http://vixra.org/abs/1209.0010 ABSTRACT: A non-unitary quantum theory describing the...
  20. E

    A question in the derivation of work done

    In our formulation of work done by a Force we say it is ∫ F.dl ... My knowledge of integration means adding Infinitesimal parts. We write dl because it is the smallest part of the distance moved. My question is why have we written F and not dF... Thanks for clarifying!
  21. dexterdev

    Can any one give me the derivation of this series

    Hi PF, I have 2 doubts : 1. Can anyone give me the derivation of series below : X = 1 + 2n + 3 n^2 + 4 n^3 + ..... 2. I can do this series reverse if the result is given, using Mc'laurin series, but then came doubt regarding derivation of Taylor series. How do...
  22. B

    Derivation of Lagrange Family of Interpolation functions

    Folks, I am puzzled how the linear interpolation functions (see attached) were determined based on the following equation below ##\displaystyle...
  23. M

    Derivation for Time to Max Radioactivity Transient Equilibrium

    Hi, I'm having a bit of difficulty deriving the time to max activity for the case of transient equilibrium for a parent-daughter. This is where I want to get to , tm = (1 / (λ1-λ2)) * 1n(λ1/λ2) I believe there is an alternative equation for tm as well expressed in terms of half-life...
  24. D

    Short Lorentz derivation problem …

    I had 1 year ago a little discussion with DaleSpam about the short Lorentz derivation (triangle) if a photon alone can be seen as a light beam. 1) The long Lorentz derivation seems me correct, so no discussion about that 2) For the short Lorentz derivation with the triangle (c.t , v.t and...
  25. R

    Lagrangian mechanics - derivation doubt.

    In the attached snip, the last few steps of the lagrangian equation is shown. I don't understand how the \frac{\delta V}{\delta\dot{q_j}}= 0. As an example let me take gravitational force. With change in velocity ( along the downwards direction obviously), there sure is a change in gravitational...
  26. H

    What's wrong with this derivation for rotational energy of a sphere?

    First, energy of a disk: \int \frac{dm}{2}r^2 \omega^2 =\frac{\omega^2}{2}\int_0^R m\frac{2 \pi r dr}{\pi R^2}r^2 =\frac{m\omega^2}{ R^2}\int_0^R r^3 dr=\frac{m\omega^2 R^2}{4 } Which agrees with other sources. However, in the following lies my problem: The equation for a circle...
  27. B

    Derivation Of The Energy Stored In A Capacitor

    Hello, I am currently reading about the topic mentioned in the title of this thread. For the most part, I understand the derivation; however, at the end of the derivation, the author adds one little condition: "Where is the energy in a parallel plate capacitor actually stored? Well, if we...
  28. F

    How is equation 15.14 derived in the wave speed derivation?

    With reference to this diagram, my textbook tells me the following: I am able to follow the rest of the derivation after this point, but I do not understand where equation 15.14 came from? I'm trying to think in terms of small angle approximations, but nothing is really coming of that...
  29. C

    Accelerated reference frames equation derivation question

    my question comes from the portion of the derivation regarding evaluating the rate of change of the principle axis vectors. this begins by supposing a vector, Q, is rotating about axis n by δθ. Specifically, my question is how from step 4 to step 5 the approximation becomes an equality. Q'...
  30. C

    Accelerated reference frames equation derivation question

    My question regards how the approximation becomes an equality.
  31. M

    Kalman smoother derivation subsitution

    Hi I am working through the derivation of Kalman smoothing and am stuck on probably a simple substitution problem for the conditional variance of the hidden state x_{t}|x{t+1}, conditioned on all previous observations Firstly the variance is given by...
  32. S

    What is the Derivation of Work in Classical Dynamics?

    Homework Statement I'm working through a derivation for work in Thornton's Classical Dynamics but I'm stuck at one step. \begin{align} \vec{F} \cdot d\vec{r} &= m\frac{d\vec{v}}{dt} \cdot \frac{d\vec{r}}{dt}dt = m\frac{d\vec{v}}{dt} \cdot \vec{v}dt \\ &= \frac{m}{2}\frac{d}{dt}(\vec{v}\cdot...
  33. S

    Griffiths quantum harmonic oscillator derivation

    Homework Statement I am unsure as to a step in Griffiths's derivation of the quantum harmonic oscillator. In particular, I am wondering how he arrived at the equations at the top of the second attached photo, from the last equation (at the bottom) of the first photo (which is the recursion...
  34. A

    Derivation of Gravitational Potential

    Hi, The derivation of the Gravitational Potential formula, as I understand, is: W = Fd (1) W = G \frac{M_1m_2}{r^2}d (2) Substituting the Gravitational Force formula W = - \int_R^∞G \frac{M_1m_2}{r^2} \, dr (3) Integrating within the boundaries of the initial distance (R) and...
  35. A

    Impulse effects on an overdamped vibrating system derivation

    Homework Statement For a zero initial deflection and for a finite initial velocity, the time dependence of the vibration response of an overdamped system to an impulse is given by: (1) θ(t)=[I/(mω)√(ζ^2-1)][e^-(ζωt)][cosh(ω√(ζ^2-1))t] which for large values of time becomes: (2)...
  36. 7

    Born Rule Derivation: A Closer Look

    Hello, I hear a lot about the Born rule ##P = |\psi|^2## where ##P## is a probability of a particle appearing at some location and ##\psi## is a wave function. When i look at double slit experiment interference pattern it seems to me that the pattern by itself already represents the...
  37. WannabeNewton

    Derivation of gauge condition in linearized GR

    Hey there guys! So we know that in linearized GR we work with small perturbations \gamma _{ab} of the background flat minkowski metric. In deriving the linearized field equations the quantity \bar{\gamma _{ab}} = \gamma _{ab} - \frac{1}{2}\eta _{ab}\gamma is usually defined, where \gamma =...
  38. Y

    Help derivation of this equation.

    Given a wave: e(t)=\hat x E_{x0}\cos \omega t+\hat y E_{y0}\cos( \omega t+ \delta)(1) The book claimed: \sin^2\delta\;=\; \left[\frac {e_x(t)}{E_{x0}}\right]^2-2\left[\frac {e_x(t)}{E_{x0}}\right]\left[\frac {e_y(t)}{E_{y0}}\right]\cos\delta+ \left[\frac {e_y(t)}{E_{y0}}\right]^2 I can not...
  39. T

    Why is the Binomial Formula a Derivation?

    I mean the binomial formula is something of the form ##\left(a+b\right)^n## = ##\sum_{i=1}^{n}\dbinom{n}{k}a^{n}b^{n-k}## and then you have the linear map ##\psi : A \rightarrow A## which is a derivation when; ##\theta(xy) = y\theta(x) + x\theta(y)## for all x,y in A so the leibniz formula...
  40. L

    Some one me with the derivation

    Homework Statement In figure, the pulleys and the cod are light, all surfaces are frictionless, and the cord does not stretch. a) How does the acceleration of block 1 compare with the acceleration of block 2? The mass of block 2 is m2 = 1.3 kg. Derive an expression for the acceleration of...
  41. S

    How Do You Derive the Laplacian of a Bloch Wavefunction in k.p Theory?

    (maybe this should go in the math section?) Homework Statement I'm supposed to derive the k.p form of the Schroedinger equation by plugging in the Bloch wavefunction expansion. But my actual question is just about the math. Homework Equations So when I plugged Bloch into the SE, one of the...
  42. T

    Question on gravitation law derivation

    Hi, guys. I was wondering on Newton's Gravity Law derivation, and I found this page: http://www.relativitycalculator.com/Newton_Universal_Gravity_Law.shtml Everything seems clear, but the first step is just killing me, because I can't get it. Assuming small incremental changes in s...
  43. Ackbach

    MHB Useful Derivation for Labs Involving Rolling Balls Down an Inclined Plane

    Problem: In beginning mechanics physics labs, it is very often the case that you get large experimental error. This can be due to a number of factors, friction, of course, being a major player. However, it can also be the case that you might be comparing apples to oranges. For example, if you're...
  44. G

    Derivation of Hawking temperature

    Hi, my first thread. The Hawking temperature for a BH can be derived through compactifying the timelike dimension and hence identifying the time coordinate of the euclidean metric such as a periodic coordinate τ with period β. Now, very interestingly in the context of AdS/CFT correspondence...
  45. dexterdev

    Derivation of Del Operator in Spherical & Cylindrical Coordinates

    Hi all, Del = i ∂/∂x + j ∂/∂y + k ∂/∂z in x y z cordinate similarly I require to see the derivation of del in other coordinates too. Please give me a link for the derivation.
  46. M

    How Is Work Calculated in a Stretched Spring?

    Homework Statement A spring with stiffness k and unstretched length L is stretched so the elongation is d = x2 - L. A force is applied to make the final length of the spring x2. What is the work done by the force in terms of d? Homework Equations W = F * d = F*dx d = x2 - L F = k*dx...
  47. TheFerruccio

    Simplification in Schrodinger derivation

    This is not a homework question. This is not for a course. However, I got a warning for posting such questions elsewhere, so, I suppose I must post them here. Homework Statement The following is an excerpt of the derivation of the Schrodinger equation. After deriving the Klein-Gordon...
  48. B

    Question on the derivation of Intensity

    Homework Statement When deriving the intensity of an electromagnetic wave in my textbook, there was a part I didn't quite get. It's how I = Watts/m^2 becomes I= u c My textbook gave an example of a electromagnetic wave through a cylinder, with cross-section area A. In 1 second it would...
  49. H

    Uniform Circular Motion Derivation of Radial Acceleration

    Homework Statement I am trying to derive the formula a_r=\frac{v^2}{r} for uniform circular motion (for personal understanding, this is not an assignment). But am having some difficulty. I have seen other proofs, but I want to know why my approach is wrong. The Attempt at a Solution...
  50. T

    Derivation of Einstein Field Equations

    I'm reading Spacetime and Geometry: An Introduction to General Relativity by Sean M. Carrol and in the chapter on gravitation, he derives the Einstein Field Equations. Here is the part I don't get. He starts with the equation R_{\mu\nu}-\frac{1}{2} Rg_{\mu\nu}=\kappa T_{\mu\nu} Wher R_{\mu\nu}...
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