consider a particle with the wave function v(x)=N[sin(x)+sin(6x)] and the boundary condiitons 0<x<pi. Find the value...
Consider a particle confined to one dimension and positive with the wave function Nxear, x20 x<0 0 where N is a real normalization constant and α is a real positive constant with units of (length)-1. For the following, express your answers in terms of α: a) Find the normalization constant N. What are the units of your result and do they make sense? b) What is the most probable location to find the particle, or more precisely, at what z...
Consider a particle confined to one dimension and positive r with the wave function 0, z<0 where N is a real normalization constant and o is a real positive constant with units of (length)-1. For the following, express your answers in terms of a: a) Calculate the momentum space wave function. b) Verify that the momentum space wave function is normalized such that (2.4) c) Use the momentum space wave function to calculate the expectation value (p) via (2.5)
Instead of assuming that a one-dimensional particle has no energy (v(x)=0), consider the case of a one-dimensional particle which has finite, but constant, energy V(x)= V sub zero.. Show that the ID particle in a box wave functions. n(x)= A sin ((pi n x)/a). Also solve the Schrödinger equation for this potential, and determine the energies En Problem 2: Particle in a Box with Non-Zero Energy (2 points) Instead of assuming that a one-dimensional particle has no energy (V(x) =...
A particle is described by the wave function where A0. Find the normalization constant A. A particle is described by the wave function where A0. Find the normalization constant A.
help on all a), b), and c) please!! 1. A particle in an infinite square well has an initial wave function Alsin sin 4 0 < x < L otherwise s(x, t = 0) 0 (a) Find A so that the wavefunction is normalized. (b) Find '(z,t). (c) Find the expectation value(E) of the energy of ψ(x,t = 0). You may use the result mx n 2 0 1. A particle in an infinite square well has an initial wave...
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...
Extra Credit (3 points to Mideterm-2) Q1. A particle is described by the wave function (x) b(a2-x2) for -a sx s a and (x) 0 for x -a and x +a, where a and b are positive real constants. (a) Using the normalization condition, find b in terms a. (b) What is the probability to find the particle at x = +a/2 in a small interval ofwidth 0.01 a ? (c) What is the probability for the particle to be...
. A particle is subject to the potential shown below: v (x) 5 V(x)-k2, when 0 S.x S oo v(x)= oo, when-oo < x 0 2 0.5 1.5 The wave function for the ground state is Determine the normalization constant C for this wave function.
The wave function of a restricted particle on the x-axis is between x = 0 and x = 1 ψ= ax ^2 and everywhere else ψ = 0. a) Find the value of constant a b) Find the probability that the particle is between x = 0.1 and x = 0.2 c) Find the wait value for the position of the particle
A particle in an infinite square well has the initial wave function: (x,0)- A sin(x/a) (0 S a (a) (b) Determine A Find$(z,t) (Hint: You will need to break up this wavefunction into a superposition of pure states. Use orthogonality to find the coefficients.) (c) Calculate (x). Is it a function of time? (d) Calculate (H).