# Step Potential with incident and reflected waves

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1. Feb 5, 2015

### baubletop

1. The problem statement, all variables and given/known data

A woman is walking along a road. She has a mass of 52 kg and is walking at 1 m/s.

(a) She is not paying careful attention and is walking straight towards the wall of a nearby building. Assume that the wall is infinitely hard and that she can be described as a plane wave (a free particle). As she “bounces” off the wall, her incident and reflected wave functions interfere. What is the spacing of the nodes in her |Ψ|2 ?

(b) Next, she approaches a curb of height 25 cm and steps down over it. Quantum mechanically she  has a finite probability of bouncing off (being reflected off) the curb. What is her reflection coefficient?

(c) In (b) above, what is her momentum if we find that she was reflected backwards by the downward edge of the curb?

2. Relevant equations
Schrödinger (I'm guessing), general forms of solutions of incident/reflected waves?
k1 = √(2mE)/ħ
k2 = √(2m(E-v0))/ħ

3. The attempt at a solution
I've tried a couple different things to no avail... We discussed general situations with k1 and k2 but I'm totally at a loss as to how to apply it to this problem.

2. Feb 5, 2015

### BvU

Please post what you have worked out in more detail, so we can provide some guidance in this peculiar but intriguing exercise.
Offhand you can guess that a will yield puny distances and b a puny probability. h is really small in daily life !

3. Feb 5, 2015

### Orodruin

Staff Emeritus
I believe you are being asked to treat her as a point particle. The 25 cm will allow you to compute the potential difference of the step along with her mass and the value of the gravitational field. You also need to show your work and what you tried in more detail in order for us to know exactly where your problem lies.