Consider a particle trapped in a 1D box with zero potential energy with walls at x = 0 and x = L. The general wavefunction solutions for this problem with quantum number, n, are: Vn(x) = sin ( The corresponding energy (level) for each wavefunction solution is: n²h? En 8mL² a) What is the probability of finding the particle between x = L/4 and x = 3L/4 when the particle is in quantum state n = 1, 2 and 3. You can use calculator or a numerical program to do the integral. For people who want to try doing the integral by hand, the following identity will be helpful: sin²(x) = (1 – cos (2x))/2.

A particle is confined to a one dimensional box with boundaries at x=0 and x-1. The wave function of the particle within the box boundaries is V(x) 2100 (- x + ) and zero V 619 everywhere else. What is the probability of finding the particle between x=0 and x=0.621? Do not enter your final answer as a percentage, but rather a number between 0 and 1. For instance, if you get that the probability is 20%, enter 0.2.

The wave function of a particle in a one-dimensional box of width L is u(x) = A sin (7x/L). If we know the particle must be somewhere in the box, what must be the value of A?

A particle is in the ground state of an inifite square well with walls at x = 0 and x = a. Suddenly the right wall moves from x = a to x = 2a. If the energy of the particle is measured after the wall expansion, what will be the most probable value of the probability of getting this result