T-ODE T"=-w²T |X-ODE| X" = − ² X = −k² X The solutions are X (x) T(t) = = Acoskæ +B sink C coswt + D sin wt
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Q: Calculate Z for a single oscillator in an Einstein solid at a temperature T = 2TE = 2Ɛ/kB.
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How do we get the solution X(x) and T(t) ? Please explain in detail.
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- Please answer within 90 minutes. State if it is Stable or Unstable.Question 8 Suppose a random sample (X1, X2,..., X25) of size 25 was drawn from a uniformly distributed population, such that X ~ Unif(1, 5). Let A = IX;, i.e., the product of all X;. Note that all X, are independent and identically distributed.Please answer this problem
- Please answer both imagesFind parametric equations for the line through (- 10,2, – 4) perpendicular to the plane 10x+ 9y + 5z = 17. Let z= - 4 + 5t. .. X = y = 0(a) Prove the "vertical angle hypothesis" (I. 15): opposing angles are congruent if two lines cut each other. (Hint: You'll need to use postulate 4 about right angles in this case.) ) (b) Complete the proof of the Exterior Angle Theorem using section (a): illustrate why beta < alphaCalculate Z for a single oscillator in an Einstein solid at a temperature T=4TE=4ϵ/kBT=4 TE=4 ϵ/kB . The value of Z isExample of numerical instability: Take y′ = −5y, y(0) = 1. We know that the solution should decay to zero as x grows. Using Euler’s method, start with h= 1 and compute y1, y2, y3, y4 to try to approximate y(4). What happened? Now halve the interval. Keep halving the interval and approximating y(4) until the numbers you are getting start to stabilize (that is, until they start going towards zero).Consider the function v(1,2) =( [1s(1) 3s(2) + 3s(1) 1s(2)] [x(1) B(2) + B(1) a(2)] Which of the following statements is incorrect concerning p(1,2) ? a. W(1,2) is normalized. Ob. The function W(1,2) is symmetric with respect to the exchange of the space and the spin coordinates of the two electrons. OC. y(1,2) is an eigenfunction of the reference (or zero-order) Hamiltonian (in which the electron-electron repulsion term is ignored) of Li with eigenvalue = -5 hartree. d. The function y(1,2) is an acceptable wave function to describe the properties of one of the excited states of Lit. Oe. The function 4(1,2) is an eigenfunction of the operator S,(1,2) = S;(1) + S,(2) with eigenvalue zero.SEE MORE QUESTIONS