An elecetron is placed inside an infite box. Quantum Mechanics

AI Thread Summary
The discussion revolves around calculating the minimum energy and momentum of an electron placed in a theoretical infinite box, specifically one that is 0.1 nm wide. Participants clarify that the electron forms standing waves, with the first harmonic representing the fundamental frequency corresponding to the ground state. The equation L = nλ/2 is referenced, where n=1 for the fundamental wavelength. The term "infinite box" is debated, suggesting a need for precision in terminology. Overall, the focus is on applying quantum mechanics principles to derive the required calculations.
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Homework Statement



An e- is placed inside an "infinite box". If the box is .1nm wide, what is the minimum energy and momentum of the e-? Start from the fundamental wavelength and prove the equation you are using to calculate the energy and momentum.

Homework Equations





The Attempt at a Solution



Wait... What's the fundamental wavelength business?
 
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The electron in a box forms standing waves. These standing waves are called harmonics. The first harmonic is called the fundamental frequency and corresponds to the electron's ground state.

I wouldn't call that box "infinite" though.
 
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Ah cool. Then n=1 and

L=nλ/2

I got it from there. Thanks.
 

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