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eku_girl83
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Any help is much appreciated!
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No, because the whole idea here is to have you work with different boundary conditions! If you understand well the case from 0 to L, you should be able to do it from L to 3L.eku_girl83 said:Suppose there is a particle in a box (infinite square well) in the ground state. The wall begins at x=L and ends at x=3L. I need to find the probability distribution for the particle.
I know how to work this problem for a well with boundaries at x=0 and x=L. In the new problem, since the width of the box is 3L - L = 2L, can I simply say that the box dimenstions are x=0 to x=2L?
Of course but there would be no point in asking this question if you could simply do this. The idea here is that someone has already made the choice to fix the origin at a distance L to the left of the left side of the well, You have to work with that. You then must give the wavefunctions with that choice of origin. It is not as simple as having the box between 0 and L but that`s the whole idea of the question!This preserves the width and makes it much easier to use my boundary conditions to determine k (U(x) = A cos kx +B sin kx), since x = 0 makes the B sin kx term disappear.
Also, how do I determine the ground state psi (x,0)? Is it Ax for O<x<L and A(L-x) for L<x<2L?
Any help is much appreciated!
The "Particle in a box problem" is a theoretical physics problem that involves studying the behavior of a particle confined within a one-dimensional box. The particle is assumed to have no energy outside of the box and is only allowed to move within the boundaries of the box.
The "Particle in a box problem" is significant because it serves as a simplified model for understanding the behavior of quantum particles in confined spaces. It helps us understand the concept of wave-particle duality and the quantization of energy levels in quantum systems.
The "Particle in a box problem" assumes that the particle is confined within a one-dimensional box with infinitely high potential barriers, meaning the particle cannot escape the box. It also assumes that the particle has no energy outside of the box, and there are no external forces acting on the particle.
The mathematical solution to the "Particle in a box problem" is a set of allowed energy states and corresponding wave functions. These energy states are quantized, meaning they can only take on certain discrete values, and the wave functions describe the probability of finding the particle at a given location within the box.
The "Particle in a box problem" has applications in various fields, such as quantum mechanics, solid-state physics, and nanotechnology. It helps us understand the behavior of electrons in atoms and molecules, the properties of semiconductors, and the behavior of particles in confined spaces in nanoscale devices.