state (a) Find A. A particle in the harmonic oscillator potential starts out in the Y(x,0) = A[3¥。 +4¥, ]. (b) Construct (x, t) and 4(x,t)|². (c) Find (x) and (p). You may use the identity fox²e-ax² dx = 4a31 (d) Check that d dt =< dv dx wave function. , an example of Ehrenfest's theorem, holds for this (e) If you measured the energy of this particle, what values might you get, and with what probabilities?
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- Statistical Physics This is the chemical potential of an ideal gas. The second image is the answer to 4.20 problem. Please generate a solution for this problem (to validate the given answer). Thank you!4. Find all second order derivatives for the following functions. (a) f(x,y) = 2.x2 + 3xy + 2y?, (b) f(x,y) =sin (x- 2y).2) Consider a particle in a three-dimensional harmonic oscillator potential V (x, y, 2) = ;mw (x² + y² + 2®). The stationary states of such a system are given by ntm(r, y, z) = vn(x)¢r(y)vm(2) (where the functions on the right are the single-particle harmonic oscillator stationary states) with energies Entm = hw(n + l ++m + ). Calculate the lifetime of the state W201.
- 3) Consider the collection of identical harmonic oscillators (as in the Einstein floor). The permitted energies of each oscilator (E = nhf (n=0, 1, 2.0, hf. 2hf and so on. a) Calculate the splitting function of a single harmonic oscitor. What is the splitting function of N oscilator? wwww wwwwww www www b) Obtain the average energy of the T-temperature N oscilator from the split function. c) Calculate the heat capacity of this system and T → 0 ve T → 0 in limits, what is the heat capacity of the system? Are these results in line with the experiment? Why? What's the right theory about that? w w d) Find the Helmholtz free energy of this system. www ww e) which gives the entropy of this system as a function of temperature. ww wd wwww wwx + 5 x 5 Calculate the following values: a. q( – 3) : b. q(7) = q(5) = C.2. Please answer the question completely and accurately with full detailed steps.
- The Duffing oscillator with mass m is described by the non-linear second order DE d? 3 + ax + Bx° = y sin (wt), dt? where [x] = L and [t] = T. Calculate the dimensions of , B, y and w. Answer: a [B] = [w] = ||Problem 3: Chemical potential of an Einstein solid. Consider an Einstein solid for which both N and q are much greater than 1. Think of each ocillator as a separate “particle". a) Show that the chemical potential is H = -kT In (**e) b) Discuss this result in the limits N » q and N « q, concentrating on the question of how much S increases when another particle carrying no energy is added to the system. Does the formula make intuitive sense?1. (a) Simplify the following number to the r+ iy form and to the re form 3+i 2+i (b) Find the absolute value and then plot the number in the complex plane.
- plz solve the question with explanation. I will give you upvoteExplain thisQ5:1 A particle of mass m moves in a one dimensional potential U (x) where x a Sketch the potential. For E < Vo show that the energy eigenvalues are obtained from the equation VA – y² 2mVoa? tan ( y + 2 where y = ka and A= Y (Hint : Applying the boundary condition at = 0 'eliminates' the cos(kx) solution for 0 < x < a.)