Show that the wavelength predicted for a particle in a one-dimensional box of length L from the de Broglie relationship matches the wavelength predicted from solutions of the corresponding Schrödinger equation where the potential is defined as: 6. V(x)=∞ (barrier) V(x)=0 (well) V(x)=∞ (barrier) (Hint: You can do this for any value of n you want although we recommend the n=2 case).
Show that the wavelength predicted for a particle in a one-dimensional box of length L from the de Broglie relationship matches the wavelength predicted from solutions of the corresponding Schrödinger equation where the potential is defined as: 6. V(x)=∞ (barrier) V(x)=0 (well) V(x)=∞ (barrier) (Hint: You can do this for any value of n you want although we recommend the n=2 case).
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![6. Show that the wavelength predicted for a particle in a one-dimensional box of length \( L \) from the de Broglie relationship matches the wavelength predicted from solutions of the corresponding Schrödinger equation where the potential is defined as:
[Image shows a diagram with two vertical shaded regions on the x-axis, which represent barriers at \( V(x)=\infty \). The region between these barriers is labeled as a "well" with \( V(x)=0 \). The axes are labeled as \( E \) (vertical) and \( x \) (horizontal), with markers at \( 0 \) and \( L \). The shaded regions denote where the potential is infinite and impassable by a particle.]
(Hint: You can do this for any value of \( n \) you want although we recommend the \( n=2 \) case).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F369cd1d2-b44d-4aa1-92ec-a804f5577ebf%2F26d236e7-60f4-40d1-ba6c-8a6fca4ae7f7%2Fnizkkgu_processed.png&w=3840&q=75)
Transcribed Image Text:6. Show that the wavelength predicted for a particle in a one-dimensional box of length \( L \) from the de Broglie relationship matches the wavelength predicted from solutions of the corresponding Schrödinger equation where the potential is defined as:
[Image shows a diagram with two vertical shaded regions on the x-axis, which represent barriers at \( V(x)=\infty \). The region between these barriers is labeled as a "well" with \( V(x)=0 \). The axes are labeled as \( E \) (vertical) and \( x \) (horizontal), with markers at \( 0 \) and \( L \). The shaded regions denote where the potential is infinite and impassable by a particle.]
(Hint: You can do this for any value of \( n \) you want although we recommend the \( n=2 \) case).
Expert Solution
Step 1
For a box of length L and V=0 in this length, we can write Schrodinger equation
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