Write down the time independent Schrödinger equation for the harmonic oscillator potential. Then confirm that the ground state wave function (n = 0) is a solution with the energy En = (1/2 + n)hw, n = 0,1,2,3... (plug in the function, differentiate, and confirm it is a solution).

Aboxcar traveling at 12 m/s approaches a string of 5 identical boxcars sitting stationary on the track. the moving boxcar collides and links with the stationary cars and they all move off together along the track. what is the final speed of the cars immediately after the collision? (you may take the mass of each boxcar to be 18,537 kg.)

Consider an insulating crystal, made up of layers of atoms. what form would you expect the temperature dependence of the phonon heat capacity to approach at extremely low temperatures if the interlayer coupling is i)very strong (rigid coupling), and ii) very weak. explain.

Is the portion of the electromagnetic spectrum that has a frequency just above that of visible light.