Please add explanation and check answer properly before submit For a particle subjected to a harmonic oscillator potential, obtain the probability that the particle is outside the classical region, if it is in the ground state.

Check Your Understanding Suppose that a particle with energy E is moving along the x-axis and is in the region O and L. One possible wave function is (x,t)={AeiEt/hsinxL, when 0xL otherwise Determine the normalization constant.

Sketch the potential for this system, and the probability density associated with the particlein the lowest energy bound state within it. Indicate on your sketch the regions where aclassical particle with E < 0 could not exist, and state whether or not it is possible to finda quantum particle in the lowest energy bound state in that region. Explain your answerusing the information in your sketch.

A particle of mass m is coustrained to move between two concentric impermeable spheres of radii r = a and r = b. There is no other potential. Find the ground state cnergy and norinalizexd wave function.