A particle in a finite potential well has energy E, as shown below. The wave function in region II where x 0 has the form ψ_II =

Question

A particle in a finite potential well has energy E, as shown below. The wave function in region II where x > 0 has the form ψ_II =

Quizplus · Accepted Answer

The particle in region II is in a state of free motion as it has energy greater than the potential energy. The general solution for free motion is of the form Ae^(ikx) + Be^(-ikx), which can also be written as F sin(kx) + G cos(kx) using trigonometric identities. Therefore, the wave function in region II has the form F sin(kx) + G cos(kx), which matches option E.

A Particle in a Finite Potential Well Has Energy E