Consider a wave-packet of the form y(x) = e-x+7(204) describing the quantum wave function of an...
2 The wave function describing a state of an electron confined to move along the X-axis is given at time zero by Y(x,0) = Ae/ Determine, in terms of A and dx, the approximate probability of finding the electron in an infinitesimal region dx centered at a) x 0 b) x a, and c) x 2a dy In which region is the electron most likely to be found? (25 pts)
2 The wave function describing a state of an electron...
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...
1. The wave function describing a state of an electron confined to move along 2 the x axis is given at time zero by W(x, 0)- Ae o2. Find the probability of finding the electron in a region dx centered at x-: σ. You need to first determine A and consider ơ as a known number.
1. The wave function describing a state of an electron confined to move along 2 the x axis is given at time zero by...
0 is given by a gaussian wave packet Consider a free particle whose state at time t (x, 0) Ae2/a2 for real constants A, a. (a) Normalize (r, 0), i.e., find A (b) Find (r, t). You can do the integral by completing the square in the exponent to get it into the form of a gaussian (c) Compute the probability density (, t), expressing your answer in terms of the quantity w av1(2ht/ma2)2 Sketch the probability density as a...
7. Given the wave function of the 2s orbital of the hydrogen as 7 27703 200 2200 - ) exp(- ) do (1) Calculate the node position (10 pts); (2) Calculate the most probable position of the electron in the orbital (10 pts); (3) Write (do not solve) the average momentum of an electron in the 2s orbital (5! pts); (4) Write (do not solve) the equation to determine the boundary value of the probability 90% (5 pts). - f...
1) Wave function for the ground state of an harmonic oscillator is given by. (x) = A1/2 (a/T)1/4 e-ax /2 Evaluate the expectation value <x<> for this wave state (ove (Hint: Joo.co u² e-a u du = 2;. ue-au du = (1/2a) (Tc/a)2) pace)
Problem 1. Wave function An electron is described by a wave function: for x < 0 *(z) = { ce Ce-s/1(1 – e-3/4) for x > 0 : where I is a constant length, and C is the normalization constant. 1. Find C. 2. Where an electron is most likely to be found; that is, for what value of x is the prob: bility for finding electron largest? 3. What is the average coordinate 7 of the electron? 4. What...
part (e),(f) and (g)
3. Wave functions (40 marks) Consider particle described by wave function (x) = Ce-x/a for x > 0, and otherwise (C is a real and non-negative). (a) Normalise (x) and plot it (you can use a computer to plotit). (b) Calculate the probability that the particle is located within distance a from the origin. (e) Find mean value of position measurement. (d) Find mean value of momentum measurement. Hint: use the fact that (x) is purely...
Consider the harmonic oscillator wave function 1/4 where α = (-)"*. Here k, is the stiffness coefficient of the oscillator and m is mass. Recall that the oscillation frequency iso,s:,k, / m In class we showed that Ψ0(x) Is an eigenfunction of the Hamiltonian, with an eigenvalue Eo (1/2)ha a) Normalize the wave function in Eq.(1) b) Graph the probability density. Note that a has units of length and measures the "width" of the wave function. It's easier to use...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can't n take the value of 0, briefly explain C) For n-3 determine the values of x (in terms of L) that correspond to a maximum or a minimum in the wave function D) For n-3 determine the values of x (in...