(1a) The wavefunction of an infinite square well is zero anywhere outside the well (x<0 and x>a). How would you conclude

[answerhappygod]

(1a) The wavefunction of an infinite square well is zero
anywhere outside the well (x<0 and x>a). How would you
conclude that is is also zero at the boundary (x=0 and a) of the
well?
(1b) When we are solving the time-independent Schrodinger
equation of the infinite square well, the eigenvalue E is assumed
to be positive. Explain why E cannot be negative by drawing an
analogy with a classical particle. (Given that the kinetic energy
of a classical particle could not be negative)
(1c) Evaluate the commutator [p, x2 - x]