Potential Step-Down: Questions & Answers

[The thinker]

Hi,

I'd just like to know if a beam will reflect when going over a down-step potential (from v=0 to v=-V_o)

Thanks.

 

[Gokul43201]

What kind of beam? Please be more descriptive. Also, tell us what your thought are.

 

[The thinker]

The question just says a beam of particles, I didn't think it mattered to be honest.

It's just the standard QM potential step but I don't know if the incoming wave will be reflected at all when giong down the step. Intuitively I'd say no... but then this is quantum mechanics so the answer is usually the option you least expected.

Ergo I expect the wave is completely reflected just because QM is odd and I figure this is the most unexpected answer. :)

 

[DeShark]

Intuitively I'd say no... but then this is quantum mechanics so the answer is usually the option you least expected.

Well, when a beam of photons passes through a pane of glass (we could treat the pane of glass as an increase in the potential of the photons - though this isn't entirely accurate, it does produce some of the results one would expect, i.e. diffraction, reflection, etc). If you've done about thin films and anti-reflective coatings, then you know that as the light exits it is also reflected a little (a lot if the angle is large enough).

So that's my intuition from something I observe physically, but quite why it's the case I'm unsure.

 

[Gokul43201]

The question just says a beam of particles, I didn't think it mattered to be honest.

It matters that it is a beam of particles. Then we know it is a standard QM problem.

It's just the standard QM potential step but I don't know if the incoming wave will be reflected at all when giong down the step. Intuitively I'd say no... but then this is quantum mechanics so the answer is usually the option you least expected.

Ergo I expect the wave is completely reflected just because QM is odd and I figure this is the most unexpected answer. :)

Since this is no way to answer the question (and you know it), why don't you do the next best thing: write down the most general form for the wave-functions on both sides and compute the reflection coefficient?

 

[Gokul43201]

Well, when a beam of photons passes through a pane of glass (we could treat the pane of glass as an increase in the potential of the photons - though this isn't entirely accurate, it does produce some of the results one would expect, i.e. diffraction, reflection, etc). If you've done about thin films and anti-reflective coatings, then you know that as the light exits it is also reflected a little (a lot if the angle is large enough).

So that's my intuition from something I observe physically, but quite why it's the case I'm unsure.

You can't solve problems by analogy or intuition when you don't know the limits of such analogy or intuition. In any case, you've picked the wrong analogy.

This is a straightforward QM problem and there is a standard approach to solving it.