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: −ℏ22m(∂2Φn(x,y)∂x2+∂2Φn(x,y)∂y2)=EnΦn(x,y),−ℏ22m(∂2Φn(x,y)∂x2+∂2Φn(x,y)∂y2)=EnΦn(x,y), such that the solution is zero at the boundaries of a box of 'width' LxLx and 'height' LyLy. You will see that the 'allowed' energies EnEn 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: −ℏ22m(∂2Φn(x,y)∂x2+∂2Φn(x,y)∂y2)=EnΦn(x,y),−ℏ22m(∂2Φn(x,y)∂x2+∂2Φn(x,y)∂y2)=EnΦn(x,y), such that the solution is zero at the boundaries of a box of 'width' LxLx and 'height' LyLy. You will see that the 'allowed' energies EnEn 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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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:
−ℏ22m(∂2Φn(x,y)∂x2+∂2Φn(x,y)∂y2)=EnΦn(x,y),−ℏ22m(∂2Φn(x,y)∂x2+∂2Φn(x,y)∂y2)=EnΦn(x,y),
such that the solution is zero at the boundaries of a box of 'width' LxLx and 'height' LyLy. You will see that the 'allowed' energies EnEn 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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