A particle in an infinite square well that extends from z = -L/2 to x= L/2 has a wavefunction given by 27 ý = A sin -(÷-). where A is a constant. Within which of the following regions of space would you most likely find this particle, it you observed its position: a) -0.21L<1<-0. 10 L ? b) -0.10L

Given a Gaussian wave function: Y(x) = (1/a)-1/4e-ax²/2 Where a is a positive constant 1) Find the normalization (if the wave function is not normalized) 2) Determine the mean value of the position x of the particle : x 3) Determine the mean value of x? : x? 4) Determine the value of Ax = /(x²) – (x)²

16. Consider the wave function Mx) = (alT)" exp(-ax12) Calculate (x) for n = 1, 2. Can you quickly write down the result for (")?

4) Consider the one-dimensional wave function given below. (a) Draw a graph of the wave function for the region defined. (b) Determine the value of the normalization constant. (c) What is the probability of finding the particle between x = o and x = a? (d) Show that the wave function is a solution of the non-relativistic wave equation (Schrodinger equation) for a constant potential. (e) What is the energy of the wave function? (x) = A exp(-x/a) for x > o (x) = A exp(+x/a) for x < o