Fermi Question - quantum tunnelling of a person

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Homework Help Overview

The discussion revolves around the concept of quantum tunneling, specifically the hypothetical scenario of a person tunneling through a wall. The original poster presents a problem involving the calculation of the de Broglie wavelength of a person and the implications of this wavelength in the context of tunneling through a potential barrier.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss calculating the de Broglie wavelength and its significance, with some questioning the feasibility of constructing a wavefunction for a person. There are considerations about the nature of the potential barrier and how to estimate the tunneling probability for individual atoms within the body.

Discussion Status

The discussion is ongoing, with various participants exploring different aspects of the problem. Some have suggested using a plane wave model for tunneling, while others express uncertainty about estimating the height of the potential barrier and the implications of an infinite barrier on tunneling probability.

Contextual Notes

Participants are grappling with assumptions about the potential barrier's characteristics and the scale of the problem, including the number of atoms in a human body and their respective tunneling probabilities.

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Homework Statement



The probability of a person quantum mechanically tunnelling through a wall

Homework Equations



The Attempt at a Solution



I'm not too sure how to approach this problem, I calculated the de Broglie wavelength of the person (mass = 60kg, velocity = 30 m/s; These values are made up by me). But then I get stuck, what can I infer from the wavelength that is calculated. I looked at the barrier potential problem, and I'm not sure how to construct a wavefunction for the person (if it is even possible? I thought of using the plane wave solution and calculating the momentum and wavenumber that appears in the complex exponential term), also the wall would represent the barrier potential (would this potential tend to infinity? like the infinite square well problem?)

My brain is melting...
 
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I guess that you have to estimate the probability for EACH single atom to tunnel through the potential barrier and then multiply all the probabilities together and get something like almost 0. However, I don't know how to calculate the energy for each atom and how many atoms our body has.
 
Sounds reasonably straightforward to use a plane wave type tunneling problem as a model. But I have no clue how you are supposed to estimate the height of the potential barrier. If it's infinity, there is no tunneling.
 
I know this is cheating but I found the answer here http://physuna.phs.uc.edu/suranyi/Modern_physics/Lecture_Notes/modern_physics6.html
 
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