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
The wave function of a restricted particle on the x-axis is between x = 0 and...
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 represented by the following wave function: ψ(x) =0 x<−1/2 ψ(x) =C(2x + 1) −1/2 < x < 0 ψ(x) =C(−2x + 1) 0 < x < +1/2 ψ(x) =0 x > +1/2 (a)Evaluate the probability to find the particle between x=0.19 and x=0.35. (b) Find the average values of x and x2, and the uncertainty of x: Δx=√(x2)av-(xav)2 xav= (x2)av= Δx =
3. At time t-0 a particle is represented by the wave function A-if 0 < x<a ψ(x,0) = 0 otherwise where A, a, and b are constants. a) Normalize ψ(x,0). b) Draw (x,0). c) Where is the particle most likely to be found at t-0? d) What is the probability of finding the particle to the left of a? e) What is the expectation value of x?
A particle is completely confined to one-dimensional region along the x-axis between the points x = ± L The wave function that describes its state is: SP 10 elsewhere where a and b are (as yet) unknown constants that can be expressed in terms of L Use the fact that the wave function must be continuous everywhere to solve for the constant b. The square of the wave function is a probability density, which means that the area under that...
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...
Please include explanations I. The graph shows the wave function ψ(x) of a particle between x =0 nm and x-2.0 nm. The cvx 0to 2.0 nm probability is zero outside of this region. In other words,p(x) - a) Find c, as defined by the figure. P(x) b) What is the probability of finding a particle between 1.0 nm and 2.0 nm? c) What is the smallest range of velocities you could find for an electron confined to this distance of...
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...
The initial wave function of a free particle is: Ψ(x,0) = A, for |x| = 0, otherwise where a and A are positive real numbers. The particle is in a zero (or constant) potential environment since it is a free particle a) Determine A from normalization. b) Determine φ(p) = Φ(p,0), the time-zero momentum representation of the particle state. What is Φ(p,t)? Sketch φ(p). Locate the global maximum and the zeros of φ(p). Give the expression for the zeros (i.e.,...
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...
4) (a) In a double-slit experiment with distance 0.0235 mm between the slits and using light with wavelength 485 nm, what is the distance from the second-order bright fringe to the fifth-order bright fringe if the screen is situated 1.80 m away from the slits? 2/L sin(8mz/L) for 0 < x < L with L a constant, and it is 0 everywhere else. Find the probability of finding the particle in the region (b) The wave function of a particle...