Consider a particle of mass m subject to a one-dimensional potential of the form kr? for z > 0, V(z) = 00 for r < 0. a. What is the ground state energy? b. What is the expectation value (a*) for the ground state?

Q1. Consider the finite square well potential shown in the following diagram: U(x) E>0 L The potential is given by: for xL| -U. for 0 0is incident on this region from the left. Using the plane A particle with energy wave approximation for the particle: a) Show that Y = Ae*+Be¬k* is a suitable general solution to the time-independent Schrödinger wave-equation (TISE) that applies in the region x L write down the four equations arising from the boundary conditions that apply at x=0 and x=L .

A particle is described by the wavefunction Ψ(t, x), and the momentum operator is denoted by pˆ. a)  Write down an expression for the differential operator pˆ. b)  Write down an expression for the expectation value of the momentum, ⟨p⟩. c)  Write down an expression for the probability density, ρ. d)  Write down an expression for the probability of finding the particle between x = a and x = b.

A particle of mass m is moving in one-dimension in a potential V (x) with zero energy. The wave function for the particle is Þ(x) = Axe-x²/a? Where A and a are constants a) Use Schrodinger equation to find the potential energy V (x) of the particle. b) Evaluate your answer at x = 0