One-Dimensional Time-Independent Schrodinger

Please see attached file.

Calculate the Zero Point Energy

A baseball is confined between two thick walls at a distance. 0.5M a part. calculate the zero point energy of the baseball. My book has no examples for zero point energy and it might be on my test. I need a outline of the solution please.

What is the probability that the electron will tunnel through a barrier?

An electron is accelerated through potential difference of 3eV and is incident on a finite potential barrier of height 5eV and thickness 5x 10^-10m. What is the probability that the electron will tunnel though the barrier. I am not 100 percent sure how to do this so a detailed solution would be helpful.

Hermitian operator

The operator F is defined in the attached file, where a is a nonzero constant. Determine whether or not F is a Hermitian operator. An outline would be helpful.

Derive an order of magnitude estimate for a harmonic oscillator

The oscillation frequencies of a diatomic molecule are typically 10^12hz-10^14Hz. Derive in order of magnitude estimate for the harmonic oscillator constant K for such molecules. I need to know how to do this for a test tomorrow. So detailed solutions please.