pls solve all steps thanks

6. The "half-baked well" potential is shown here: a. Which of the wavefunctions below is the correct for region I and why? (2 pt) 1.cos(k1x)2.sin(k1x)3.eikk1x4.eikk1x b. In the 1st region where V=0, then: 2m2k12I(x)=EI(x) Solve for k1 and 1(x) in this case. Hint: this is just an algebra problem. (2 pts) c. In the 2nd region where V=V0, (meaning it's just a value with no " x " dependence) then: 2m2k22II(x)=(EV0)II(x) Solve for k2 in this case. (2 pts) d. The wavefunction II(x) is in a region of constant potential, therefore possible wavefunctions are: 1.cos(k2x) 2. sin(k2x) 3. eik2x 4. eik2x Figuring out which one is correct is a bit harder. Here is how you reason through it: If a particle starts at 0 and moves to the right, it will hit the wall. If the particle passes through the wall into region 2, it will continue moving to the right, and do so forever, since there are no more walls to bounce off of. Therefore, which of the functions above (1-4) correctly describe a particle always moving right? (2 pts) e. Since k2=2m(EV0) there are two possible wavevectors for region 2 because the particle may have more energy that the potential barrier or it may have less. If E>V0, then 1I(x)= the following: k2=2m(EV0)=?2m(V0E) f. If plug k2 above into II(x)=ei2x, and simplify, can you show that the wavefunction should not oscillate as it moves to the right but instead decay to nothing inside region 2 ? (2 pts)