Time evolution of the wavefunction of a particle in a square well

See attached file.

Quantum probability, probability current, commutators

(See attached file for full problem description)

Harmonic oscillator problems.

See attached file.

what are the minimum and maximum values of the coordinates of the respective classical oscillator with a given energy E?)

In the ground state of the harmonic oscillator, what is the probability (correct to three significant digits) of finding the particle outside the classically allowed region? (Hint: what are the minimum and maximum values of the coordinates of the respective classical oscillator with a given energy E?) Look in math tables under “Normal distribution” or “Error function” for the numerical value of the integral.

Two well problem.

See attached file.