Part 1 a. Calculate the relative probability distribution, PR(X), for a 1-kg particle initially at rest and attached to a spring (a harmonic oscillator) of spring constant k = 2 N/m and an initial displacement from equilibrium of 1 m. b. Now enter in this function into the text box and set the proper classical limits by clicking the "change limits and evaluate" button. What is the normalized classical probability distribution, PN(X)? You must normalize (a) by doing the integral.

There is an electron, in a 1-d, infinitely deep square potential well with a width of d. If it is in ground state,  1. Draw the electron's wavefunction. Show the position of the walls of the potential well. 2. Explain how the probability distribution for detecting the electron at a given position differs from the wavefunction.

Consider a finite potential step with V = V0 in the region x < 0, and V = 0 in the region x > 0 (image). For particles with energy E > V0, and coming into the system from the left, what would be the wavefunction used to describe the “transmitted” particles and the wavefunction used to describe the “reflected” particles?