Question

When solving 1-D shrodinger equation particle in box question, why do people set general solution as Y=Aexp(ikx)+Bexp(-ikx) instead of Y=Aexp(ikx)? When do i need to use the latter one?

Answer 1

it includes the simplest example of a scattering phenomenon in which a beam of particles is “deflected” by a local potential. Moreover, this one-dimensional geometry also provides a platform to explore a phenomenon peculiar to quantum mechanics – quantum tunneling.

. after the encounter with the barrier, the transmitted wavefunction undergoes only a change of amplitude (some particles are reflected from the barrier, even when the energy of the incident beam, E, is in excess of V0) and a phase shift.

we use latter solution in the region after the barrier , as there will be transmitted wave only in that region in positive x direction.

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