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  1. V

    De Broglie wavelength in terms of accelerated potential difference

    Problem: Derive a formula expressing the de Broglie wavelength (in Å) of an electron in terms of the potential difference V (in volts) through which it is accelerated. Solution (so far): The textbook's answer is the following, \lambda=12.27[V(\frac{eV}{2m_{0}c^{2}}+1)]^{-\frac{1}{2}} I'm...
  2. J

    Energy governing equation in terms of PRESSURE

    Hi all, I derived the energy equation for compressible flow in terms of pressure p from the governing equation in terms of the total energy density e (using the perfect gas assumption and assuming constant viscosity), but I am not sure if I did it correctly. I post it here, please tell me if...
  3. E

    Simplifying Additive Exponential Terms

    Homework Statement I have developed an equations for calculating some pollutant concentration as a function of x and y. I'm trying to simplify the problem so that I can write the equation for wp as a function of x. All variables except x and wp are known. Homework Equations...
  4. Duderonimous

    Cases in which constants can absorb terms

    Homework Statement What are the cases in which constants of integration can and cannot absorb terms and operations and just be redefined as c. Homework Equations The Attempt at a Solution As long as I keep redefining my constant of integration I can say -c=k ac=k where...
  5. L

    Uncertainty principle in terms of expectations values in Dirac notatio

    Homework Statement Show that (\Delta A)^{2} = \langle \psi |A^{2}| \psi \rangle - \langle \psi |A| \psi \rangle ^{2}\\ \phantom{(\Delta A)^{2} }=\langle \psi | (A - \langle A \rangle )^{2} | \psi \rangle , where \Delta A is the uncertainty of an operator A and \langle A \rangle is the...
  6. K

    Geometric series with modified terms

    I am looking for a way to sum some numbers. I understand that if I want to sum pi, I can use the geometric series: \sum\limits_{i=0}^N p^{i} = \frac{1-p^{N+1}}{1-p} But can anyone help me with what to do when I need: \sum\limits_{i=0}^N p^{i} q^{ti} where t is just a constant...
  7. Y

    Finding the Tension in terms of weight and the angle of incline

    Homework Statement Two blocks, each with weight ω, are held in place by a frictionless incline. In terms of ω and the angle θ of the incline, calculate the tension of the rope connecting the two blocks. Homework Equations ƩF=ma The Attempt at a Solution Since it is on a tilted...
  8. Fantini

    MHB Continuity in terms of closed sets

    Hello. I wish to prove this: $$\text{A function } f: X \to Y \text{ is continuous if and only if the inverse image of any closed set is closed.}$$ Proof: $(\implies)$ Let $V \subset Y$ be a closed se. By definition, $Y-V$ is an open set, and by the continuity of $f$ it follows that...
  9. B

    Linear approximation higher order terms

    My questions are from lecture 9, MIT OCW SV Calculus, Jerison, 2009; At 27:50 he is deriving the linear approximation for the function e^(-3x)(1+x)^(-1/2)≈(1-3x)(1-1/2x)≈1-3x-1/2x+3/2x^2≈1-7/2x, for x near 0. In the last step he drops the x squared term since it is negligible(no questions so...
  10. C

    The Terms Potential & Potential Difference

    So I'm supposed to read Chapter 34 (Electric Current) in the next couple of days. I'm sure I'll have more questions about it but one question I have right now is what does the book mean by the term potential and potential difference. My teacher briefly explained it but I couldn't stay awake this...
  11. D

    Terms in the Yang-Mills Lagrangian

    I've been doing some self-study in Peskin and Schroeder and been struggling a bit in Part III. Right now, I am stuck on the last two terms in 16.6 (Lagrangian for Yang-Mills). Presumably these come from (-1/4) (F^{a}_{\mu\nu})^2, but I am getting stuck on getting the indices to work out...
  12. N

    Equation with logarithmic and polynomial terms

    This is not actually a homework question, but it seemed appropriate to put it here. In an old exam from 1921 I found the following problem. I never learned how to solve this type of thing and I haven't been able to figure it out, so: how does one solve this? Homework Statement Solve for...
  13. L

    How do you make y= sin(sqrt(5x + 3)) in terms of y? :/

    1. Yes, I don't know this. =.= So how to you move sine to the y side? You can't say: arcsin(y) = sqrt(5x + 3), can you...? I don't know how to move the sin! Help! Thank you! :)
  14. J

    Simple equations in Dirac Delta function terms

    Hi there, I'm trying to comprehend Dirac Delta functions. Here's something to help me understand them; let's say I want to formulate Newton's second law F=MA (for point masses) in DDF form. Is this correct: F_i = \int [m_i\delta (x-x_i) a_i\delta (x-x_i)]dx Or is it this: F_i = [\int...
  15. J

    How do you indicate transient terms when y just equals 1 ?

    how do you "indicate transient terms" when y just equals 1 ? t is the dependent variable in this problem and I'm told to "indicate transient terms". Well, t=1 so is this a trick question or did I do something wrong?
  16. F

    Standard Deviation in terms of Probability Function

    Homework Statement I've still yet to learn Latex since I'm pretty good with words equation editor, so here's the question typed out in words. Homework Equations I really don't know what to do here. The Attempt at a Solution
  17. P

    Express this series in terms of the given series A(x)

    Homework Statement Let A(x) = a0 + a1x + a2x2 + a3x3 + ... = Ʃanxn. Express E(x) = a0 + a2x2 + a4x4 + ... = Ʃa2nx2n. Do the same for O(x) = a1x + a3x3 + a5x5 + ... Homework Equations A(x) = a0 + a1x + a2x2 + a3x3 + ... = Ʃanxn The Attempt at a Solution So I tried using A(x2)...
  18. T

    Clarification of electrical terms

    I am embarrassed to be asking such an elementary question, but I want someone to explain the difference between amps, watts, and joules. I tried a dictionary, but it wasn't specific enough.
  19. J

    MHB Sum of first m terms of a combinatorial number

    Dear Math Help Boards, I have a tricky problem that I hope one of you can help me with. (It's for a personal project, nothing to do with school.) I'm looking for a closed-form expression for the sum of the first through m-th terms of a combinatorial number. For those of you unfamiliar with...
  20. J

    Closed form expression for sum of first m terms of a combinatorial number

    Dear Physics Forums denizens, I have a tricky problem that I hope one of you can help me with. (It's for a personal project, nothing to do with school.) I'm looking for a closed-form expression for the sum of the first through m-th terms of a combinatorial number. For those of you...
  21. H

    Oscillator with third and fifth order terms?

    We usually only consider the first order term for an oscillation, are there any papers on extending that model and including third and fifth order terms (since only odd power terms would cause a periodic motion)? The ODE would look like x''=-αx-βx^3+O(x^5)
  22. D

    How many terms are needed in the series 11+16+21+26 + to exceed 450

    Homework Statement How many terms are needed in the series 11+16+21+26...+ to exceed 450 d=5 Homework Equations Sn=n/2(2u1+(n-1)d) The Attempt at a Solution (455 because is term exceeding 450 by the d of 5) 455=n/2(22+5n-5) 455=17n+5n2 455/17=5n2 Calculator work, but...
  23. A

    Newton's third law in terms of inertial position vectors for n-body system

    Assuming $$\vec{r_{a}}$$ and $$\vec{r_{b}}$$ is calculated from an inertial frame of reference. then for any two objects (named a and b) in a system of more than two objects, Is this the Newton's third law, $$\frac{d^{2}}{dt^{2}}m_{a}\vec{r_{a}}=-\frac{d^{2}}{dt^{2}}m_{b}\vec{r_{b}}$$...
  24. P

    Expressing sol. of Poisson eqn. in terms of vol. and sur. integrals.

    Hi, Referring to Jackson's Electrodynamics 3ed, page 197, line 5. He assumes that the magnetization can be divided into volume part and surface part, thus generating eqn 5.100. This is fine. In a straightforward way, I wanted to do the same but for electrostatics, eqn 4.32:∅= (1/4πε) ∫dv...
  25. B

    Can Someone Explain What String Theory Is? (Simple Terms With Examples)

    Can Someone Explain What String Theory Is? (Simple Terms With Examples) Ive been hearing a lot of references to this new string theory, what is it?
  26. F

    First nonzero terms of Fourier sine series

    Homework Statement Consider the function φ(x) ≡ x on (0, l). Find the sum of the first three (nonzero) terms of its Fourier sine series. Reference: Strauss PDE exercise 5.1.3 Homework Equations The Attempt at a Solution I have found the coefficient without difficulty, it is...
  27. D

    How to express Jump Process in terms of the generator (rate matrix) A

    Hi Guys I have problem to express the jump process as following ways. Please let me know your ideas~! Thank you so much. ------------------------------------------------------------------------- Let (Xt)t≥0 be an irreducible continuous-time jump process on a nite state space...
  28. P

    What is the energy ordering for d4 ions in a crystal field?

    The relative ordering of energy in the crystal field of d4 ions are arranged as 4A1g, 4T2g and 4T1g. How can I determine this? What is the rule for describe the relative energy of the terms for dn ions?
  29. C

    Derivation of the kinetic energy equation in terms of distance.

    I have seen the derivation of the kinetic energy equation using F=M*v' and E=F*x And I can see how this works, however if you try to do this without thinking about velocity, and only thinking about the rate of change of distance, and the rate of change of rate of change of distance, then the...
  30. L

    How to factor 3rd degree polynomial with 3 terms

    -x^3+12x+16 Every single technique I read about online of how to factor 3rd degree polynomials, it says to group them. I don't think grouping works with this. I tried but it didn't work, since there's only 3 terms. Apparently I'm not supposed to have a cubic variable without a squared...
  31. W

    Solve relativistic velocity in terms of momentum (vector equation)

    Given the formula \vec{p}=\frac{m_0}{\sqrt{1-\frac{|\vec{v}|^2}{c^2}}}\vec{v}, I'd like to make \vec{v} the subject, so I can do a numerical approximation for some relativistic motion problem. I want to treat it as a vector equation, but since it is non-linear, the only way I can think of is to...
  32. H

    Evaluate the integral by interpreting it in terms of areas.

    Homework Statement from [-2,2] rad(4-x^2) Homework Equations The Attempt at a Solution I know its a circle and i get the equation to be y^2+x^2=4 and I believe it has to be divided into a circle and rectangle so the area of the rectangle i got to be 2 the circle i got to be...
  33. A

    Ranking springs in terms of spring constant

    Homework Statement Homework Equations Hooke's law. F = kΔx ω = sqrt(k/m) The Attempt at a Solution For part A F = mg = kΔx k = mg/Δx g is a constant so the spring constant is proportional to the mass and inversely proportional to the change in distance that the spring...
  34. T

    Why not formulate QM in terms of |ψ| squared?

    I'm beginning to study QM, and as I understand all the information we can get out of system with 1 particle is the probability distribution function (which has position and time as variables). By knowing the wave function it's possible to know the probability distribution function, but that's an...
  35. U

    Solving Summations of n.n! Terms

    Homework Statement 1.1!+2.2!+3.3!...n terms Homework Equations The Attempt at a Solution The first part of every term is in AP whose cd is 1. Also the nth term of this series is given as n.n! If I expand it it becomes n.n(n-1)(n-2)...1 Now S_n=\sum t_n \\ = \sum n.n(n-1)(n-2)...1...
  36. M

    Power in terms of work and energy

    Is power a quantity defined by: \frac{dU}{dt} and \frac{dW}{dt} Is it just defined to be it, or can it be derived in terms of the other (I mean, dU/dt in terms of dW/dt and vice versa)? I now there's physical motivation to it, but sometimes I just can't help trying to ponder how these equations...
  37. G

    Shape of Kerr event horizon in terms of reduced circumference

    The event horizon of a Kerr black hole is often depicted as being spherical, but this seems to be a reference to the horizon as defined in Boyer-Lindquist coordinates, where horizons appear at a constant value of r. However, Thorne describes the "black hole's horizon bulg[ing] out at its...
  38. Spinnor

    Can the electromagnetic vector potential be written in terms of a complex field?

    Is there a complex field that when properly interpreted yields the four components of electromagnetic vector potential, A_0, A_1, A_2, and A_3? Somewhat along the lines of the complex field ψ yielding information about a particles energy, momentum, and position probability. Thanks for any...
  39. J

    Showing Momentum and Kinetic Energy In Terms of a Singular Formula

    Homework Statement Click to enlarge Homework Equations K= 1/2 mv12 + 1/2mv22 p= m1v1 +m2v2 The Attempt at a Solution I have pages and pages of trying to simplify/work backwards and nothing is working!
  40. B

    How Do I Translate These French Math Terms?

    Hi, All: Sorry if this is off-topic, but I did not know where else to ask. These are geometric/topological terms, so I thought it'd make sense to ask here: I am reading a math paper in French, and I'm having trouble : 1)Cellulation de Contact . Cellules. I suspect this has to see with...
  41. Q

    Solving equation in terms of symbols

    Hi friends I want to solve an equation which is function of x,y,z,m but i want to find answer like this m=... i want my answer(m) to be a function of x, y, z but when i solve it in MATLAB or mathematica none of them give me the answer I know that my equation must have 4...
  42. L

    Infinte number of terms from a sequence in a sub-interval

    I have across the following argument, which seems wrong to me, in a larger proof (Theorem 4 on page 9 of the document available at http://www.whitman.edu/mathematics/SeniorProjectArchive/2011/SeniorProject_JonathanWells.pdf). I would appreciate if someone can shed light on why this is true...
  43. M

    What does phase of the motion in terms of cosine displacement mean?

    What does "phase of the motion in terms of cosine displacement" mean? I'm getting tripped up on the wording of this homework question. Homework Statement Measured acceleration: An accelerometer has measured the simple harmonic motion shown in the image below. Homework Equations You...
  44. J

    Correct interpretation of terms in proper velocity expression?

    The "cosmological" proper distance from the origin, D(t), to an object at radial co-ordinate r at cosmological time t is given by D(t) = a(t) r(t) The corresponding "cosmological" proper velocity v of the object is given by v = \frac{dD}{dt} = \frac{da}{dt} r(t) + a(t) \frac{dr}{dt} Using...
  45. B

    Continuity Equation: Relationship between vA and vB in terms of d and D

    Homework Statement The continuity equation provides a second relation between the vA and vB, this time in terms of the diameters d and D. Numerical check: If the diameters are d = 1 cm and D = 10 cm, what is the ratio of the speeds, vB/vA? Homework Equations To clarify, is both d and D...
  46. skate_nerd

    MHB Volume of a torus, in terms of big radius R and little radius r, washer method

    This problem is really making my head spin. I'm in university calculus II and my teacher loves giving us extra homework that is supposed to really challenge us. This is problem 1 of 5. "Let 0<r<R and x2+(y-R)2=r2 be the circle centered at (0,R) of radius r. Revolving the disk enclosed by that...
  47. N

    Rearranging terms of a conditionally convergent series

    Why the heck will the sum of such a series going towards infinity change if its terms are re-arranged? My book omits the proof, and without it this claim makes no sense to me. Can somebody provide an example of such a series, and maybe some light explanation (I'm way too exhausted for heavy...
  48. T

    Maple Calculating Time Derivatives of Terms with Autonomous Systems

    Hi guys I have 5 term which each term includes three function of time (autonomous system ), i want to obtain time derivative of each term as other terms for example if i define each term as a dimensionless variable , e.g. x , y , z , v , w , i want to know dx/dt = as a combination of x , y ...
  49. Z

    Expanding atomic displacements in terms of all lattice wave modes?

    I find the expression: "In general, one can expand the atomic displacements in terms of all the lattice wave modes (resembles a Fourier series expansion)" at: https://courses.cit.cornell.edu/ece407/Lectures/handout17.pdf But I have not found the expression in any other literature. (In fact...
  50. shounakbhatta

    Understanding Co & Contra Variants, Coordinate Free System & Parallel Transport

    Hello All, I am new to GR, studying slowly. I am little bit confused between the following terms and their usage: (a) Co & contra variant vectors - Do they help in transformation? (b) What is a co-ordinate free system? Do co & contra variant vectors help it? (c) What is parallel...
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