Use the method of separation of variables to construct the energy eigenfunctions for the particle trapped in a 2D box. In other words, solve the equation: -h? ( a?»(x, y) + a²ª„(x, y) dy? En Pn (x, y), 2m dx² such that the solution is zero at the boundaries of a box of 'width' L, and 'height' Ly. You will see that the 'allowed' energies En are quantized just like the case of the 1D box. It is most convenient to to place the box in the first quadrant with one vertex at the origin.
Use the method of separation of variables to construct the energy eigenfunctions for the particle trapped in a 2D box. In other words, solve the equation: -h? ( a?»(x, y) + a²ª„(x, y) dy? En Pn (x, y), 2m dx² such that the solution is zero at the boundaries of a box of 'width' L, and 'height' Ly. You will see that the 'allowed' energies En are quantized just like the case of the 1D box. It is most convenient to to place the box in the first quadrant with one vertex at the origin.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 31E
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![Use the method of separation of variables to construct the energy eigenfunctions for the particle trapped in a 2D box. In other words, solve the
equation:
-h? ( 020, (x, y)
a²¤n(x, y)
En P, (x, y),
2m
dx?
dy?
such that the solution is zero at the boundaries of a box of 'width' L, and 'height' Ly. You will see that the 'allowed' energies En are quantized
just like the case of the 1D box. It is most convenient to to place the box in the first quadrant with one vertex at the origin.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd9ee4f1-fd19-476d-ab76-bb676278a043%2F5f4b2836-fb23-4f2a-83ba-696c3afa98cf%2Flrmt2q_processed.png&w=3840&q=75)
Transcribed Image Text:Use the method of separation of variables to construct the energy eigenfunctions for the particle trapped in a 2D box. In other words, solve the
equation:
-h? ( 020, (x, y)
a²¤n(x, y)
En P, (x, y),
2m
dx?
dy?
such that the solution is zero at the boundaries of a box of 'width' L, and 'height' Ly. You will see that the 'allowed' energies En are quantized
just like the case of the 1D box. It is most convenient to to place the box in the first quadrant with one vertex at the origin.
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