Step Potential with incident and reflected waves

In summary, a woman with a mass of 52 kg and walking at 1 m/s is walking towards a wall and a curb. When she bounces off the wall, her incident and reflected wave functions interfere, and the spacing of the nodes in her |Ψ|2 is determined. When she steps down over the curb, there is a finite probability of her being reflected off of it, and her reflection coefficient can be calculated. If she is reflected backwards by the downward edge of the curb, her momentum can be determined. To solve these problems, the Schrödinger equation and general forms of solutions of incident and reflected waves can be used, along with the equations k1 = √(2mE)/
  • #1
baubletop
28
0

Homework Statement



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?

Homework Equations


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

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.
 
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  • #2
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
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.
 

Related to Step Potential with incident and reflected waves

1. What is a step potential?

A step potential is a sudden change in potential energy at a particular point in space. It can occur in various physical systems, such as an electronic circuit or a quantum mechanical system.

2. How does a step potential affect incident and reflected waves?

When a wave encounters a step potential, it can be partially transmitted and partially reflected. The transmitted wave will have a different amplitude and phase compared to the incident wave, while the reflected wave will have the same amplitude but opposite phase.

3. What is the relationship between the incident and reflected waves in a step potential?

The incident and reflected waves in a step potential are related by the law of conservation of energy. This means that the sum of the incident and reflected energies is equal to the total energy of the system.

4. How does the height of a step potential affect the behavior of incident and reflected waves?

The height of a step potential determines the amount of energy that is reflected and transmitted by the wave. A higher step potential will result in a greater reflection and a smaller transmission of the wave.

5. Can a step potential create interference patterns?

Yes, a step potential can create interference patterns when the transmitted and reflected waves interfere with each other. This results in regions of constructive and destructive interference, which can be observed as a pattern of varying amplitudes in the transmitted wave.

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