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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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