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) -...
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...
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...
What is the probability of finding a particle between x = 0 and x = 0.25 nm in a box of length 1.0 nm in (a) its lowest energy state (n = 1) and (b) when n = 100. Relate your answer to the correspondence principle. This is an illustration of the correspondence principle, which states that classical mechanics emerges from quantum mechanics as high quantum numbers are reached. What does this all mean? • Only certain (discrete) energies are...
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...