I'm a high school student at East Mecklenburg HS in North Carolina. I'm working on some quantum physics problems as part of a non-graded extra assignment for a higher-level physics course offered at my high school. Our teacher has said we can ask anyone, besides fellow students, for assistance as long as we can solve the problems and explain the solutions. The assignment isn't for a grade, and is more to see if any of us can do it than anything else. If you have the time, I hope you can offer some insight into these questions: -------------------------------------------------------------------------------------------------- Q1) A particle of mass "m" and charge "q" is confined to a one dimensional box whose sides at x=0 and x=a. A measurement of the energy shows that the particle is in the second (first excited) energy eigenstate. At time t=0 the wall at x=a is suddenly moved to x=b with b>a/ a) find the relation between a and b so that the energy is unchanged. b) find the probability that the energy remains unchanged. Q2) An atom with no permanent magnetic moment is said to be diamagnetic and has an induced diamagnetic moment mu=-d(DELTA E)/dB where DELTA E is the change in energy when the atom is placed in a magnetic field B. Find the induced diamagnetic moment for the hydrogen atom in its ground state when a weak magnetic field is applied. (Note the derivative is a partial derivative.) Q3) A particle of mass "m" and charge "q" is confined to a one-dimensional box whose sides are at x=0 and x=a are conductors. Thus, when a voltage is applied to the two walls, the particle experiences a uniform electric field of amplitude E_0. If this voltage is applied at t=0, when the particle is in the ground state, find an expression giving the probability that after a long time the particle has made a transition to the nth excited state. Evaluate this expression for n=2. Q4) The two dimensional oscillator Hamiltonian (see hamiltonian.pdf). When perturbation of H'=lambda*(m*omega^2)(xy) with lambda much less than one is applied, find the first order energies and the corresponding appropriate zero order energy eigenstates for the three degernerate states |2,0>, |0,2>, and |1,1>. Q5) A plane rotator consists of a mass "m" rigidly constrained to move at a distance "R" from a fixed origin, i.e., a bead of mass "m" on a frictionless circular wire of radius "R." Schrodinger's equation for the rigid plane rotator is (see attached pdf). I=mR^2 is the rotation about the z-axis. a)Find the energy eigenvalues and normalized energy eigenfunctions. b)at time t=0, the wave function of the rotator is PSI(PHI, 0)=A*cos^2(PHI). Find PSI(PHI, t). c)The particle is given a charge of +q and a weak static uniform electric field is applied along the x axis. Find the first non-zero corrections to the energy eigenvalues. d)Consider the extreme case of a very large uniform electric field acting on the rigid plane rotator. Devise a physically plausible approach for this situation and obtain the zero order energy eigenvalues as well as the first order corrections. e) Instead of a constant electric field, an electric field pulse of the form E(t)=E_0 * e^(-gamma*t) is applied starting at time t=0. If the rotator is initially in an energy eigenstate, find the first order probability that after a long time it has made a transition to another energy state as a result of the electric field pulse. f)The electric field is removed and a static uniform magnetic field is applied along the z-axis. Find the energy eigenvalues. Email me at email@example.com and I can send you the PDF's with the equations. they're almost unreadable if typed out.