(10 points) Normalize the wave function: Find the expectation values of (x), (r aj. Ģ) and...
Problem 2 Consider the wave function Where a, λ ω are positive constants. (a) Normalize (b) Determine the expectation values ofx and x; (c) Find the standard deviation ofx. Sketch the graph of 1992, as a function ofx, and mark the points (<x> + σ) and 〈X>-07, to illustrate the sense in which σ represents the "spread" in x, what is the probability that the particle would be found outside this range?
3. If (:) is a wave function in which the expectation value of the momentum is P, then find the expectation value of the momentum i.e. <p> in the state el (po)/ \(r) (5 points).
2. Find the expectation value for <p2 > for the ground-state wave function of the infinite 1-d square well. Here p = -i(hbar) d/dx is the (linear) momentum operator
Consider a particle of mass m that is described by the wave function (x, t) = Ce~iwte-(x/l)2 where C and l are real and positive constants, with / being the characteristic length-scale in the problem Calculate the expectation values of position values of 2 and p2. and momentum p, as well as the expectation Find the standard deviations O and op. Are they consistent with the uncertainty principle? to be independent What should be the form of the potential energy...
Problem 4 For the wave function φ(x,0) = Ax(a-x) find the expectation value of Hat time ț-0 in the ID box of length .
Suppose at a certain time to the wave function is, Ψ(x,6) N for all x between the values ofx = 1 cm and x = 2 cm. For all values ofx outside the interval [12] the wave function is zero. a) Normalize the wave function. (Solve for N). Pay attention to units! b) Sketch the probability density V(x,/,)(x, as a function of x c) What is the probability of finding the electron between 1.5 cm and 2.0 cm? d) What...
3. Consider the wave function (x, t) = Ae-2 -ut Where A, 2, and are positive real constants. (a) Normalize Y. (b) Determine the expectation values of x and x?. (c) Find the standard deviation of x. Sketch the graph of V', as a function of x, and mark the points (x) + a) and (x) -o to illustrate the sense in which represents the spread" in x. What is the probability that the particle would be found outside this...
Consider a particle in a 1-d well with potential V(x) =-U for-d < x < d, and V(z) 0 elsewhere. We will use the variational wave function v(z) = A(b + r), t(x)-A(b-x), -b < r < 0, 0 < x < b, to show that a bound state exists for any U0. a) Normalize the wave function. Find the expectation values of the kinetic and potential energies b) Show that for sufficiently large b, with b> d, the expectation...
2.3 The wave function of a harmonic oscillator with the parameters m and w is a superposition of n 0 and n 2 stationary states o(Z,x ), 〈p), 〈d V(x)〉 (5 points) (a) compute the expectation values (r (b) find the expectation value and the variance of the total energy, Which value of the energy you can actually get when doing measurements and with which probability? (5 points)
##### show all steps thoroughly (sorry for my bad grammar) Assume that electron in state have wave function of spherical coordinate 4π Where g(r) wave function in part of radius By (r)|-r-dr = 1)show that wave function write in term of (theta, d) 2)find expectation of L Assume that electron in state have wave function of spherical coordinate 4π Where g(r) wave function in part of radius By (r)|-r-dr = 1)show that wave function write in term of (theta, d)...