Classical behavior, 3 dimension wave function and reflection

[Docdan6]

Homework Statement

I'm a pharmacologist and I have a modern physics course to do. This is not my field and I'm completely lost... We were given this problem to do. Thanks a lot in advance.

Consider a potential where
U(x) = 0 for x ≤ 0
U(x) = -3E for x > 0

Consider a particle of energy E incident by the left. When the particle arrives at the potential step,

1. What is the behavior of the particle from a classical point of view? How does vary its kinetic energy?
2. From a quantum point of view, assuming that the incident wave function has the form Ψ(x) = 1eikx . Determine the complete wave function in the entire space.
3. In the quantum case, what is the probability that the particle is reflected?

Homework Equations

The Attempt at a Solution

Here's what I have so far

1. I think that because E is greater than -3E, classically the particule would be transmitted completely without reflection because the difference between the energy E and the step potential would be positive, and would continue infinitely in x > 0... but I'm not sure. And its kinetic energy would not change.

2. I think that because the question ask the equation in three dimension, the forme should be:
Ψ(x, y, z) = 1 ( e^ikx + e^iky + e^ikz )
but that can't be so simple...

3. from my research I came up with this:
The reflection ratio R would be
R = (k1 - k2)² / (k1 + k2)²

k1 being √(2mE / ħ²)
k2 being √(2m(E - V0) / ħ²)

Please help me... it's been two days that I'm looking for this...Thanks !

 

[BvU]

Where do you get the idea that this is in three dimensions ?

 

[PeroK]

I'm a pharmacologist and I have a modern physics course to do. This is not my field and I'm completely lost...

1. I think that because E is greater than -3E, classically the particule would be transmitted completely without reflection because the difference between the energy E and the step potential would be positive, and would continue infinitely in x > 0... but I'm not sure. And its kinetic energy would not change.

I'm not sure how you ended up on a QM course without much knowledge of basic physics. We could probably help you on here to get to grips with some basic classical physics like question 1. But, to progress to QM, you'll need some very intensive and extensive help.

Perhaps someone else might try harder to help you, but I feel like there is only so much one can do, I'm sorry to say.