Relative states and Hidden Variables in Quantum Mechanics

I ONLY NEED HELP WITH NUMBER ONE. It looks really long but the beginning is just a set up to the question. Skip to 'Your job' to see the question. I don't understand this stuff at all so if you could guide me through this step by step it would be appreciated. Explanations are important.

A particle moving in a delta potential with positive energy

A particle of mass m, with energy E>0, is moving in the potential V(x)=g[delta(x+a) + delta(x-a)] Assuming that the particle is incident from the left, what is the solution of the Schrodinger equation in all three regions (xa) for this situation? Also, what are the appropriate continuity conditions at x=+a and x= -a?

Kinetic and potential energy of harmonic oscillator, virial theorem

(See attached file for full problem description) --- 1. Consider a particle moving in a harmonic oscillator potential V(x) = ½ kx2. A solution of the time-dependent Schrodinger equation is cn n(x)*e –i * E(n) * t / h-bar where the n are harmonic oscillator energy eigenstates. a. Calculate the energy expectation value and the kinetic energy expectation value K(t) = < | | > At any given time t, in terms of the constants cn. Show that your answers are real, even if the cn are complex. b. Let be the time average of K(t). Show that = ½ .

Concentric Spheres

(See attached file for full problem description) --- 2. A particle of mass m is constrained to move between two concentric, impermeable spheres of radii r = a and r = b. The potential V( r ) = 0 between the spheres (a

Angular States in Quantum Mechanics

(See attached file for full problem description) --- 3. Let denote the eigenstates of L2 and Lx; i.e. L2 = l(l+1)h-bar2 and Lx = m*h-bar* a. Explain briefly why you can always express any given as a superposition of spherical harmonics Yl’m’ with l’=l. b. In particular, for each m = +1,0,-1, find the constants a,b,c such that =aY11+bY10+cY1,-1 is a normalized eigenstate of Lx, and verify that , , are orthogonal. This problem should be solved algebraically, using Lx = ½ (L++L-), and the orthogonality of the spherical harmonics. c. Suppose a system is in the state . If Lz is measured what possible values could be found, and with what probabilities? Calculate the u... click for more