The electron is in an infinitely deep one-dimensional

In this problem, we consider an electron located in an infinitely deep one-dimensional rectangular potential well of width l. We need to find the probability that it is at a distance of 0.02l from the edge of the well in an excited state (n=3).

To solve this problem, it is necessary to use the formula for the probability of finding a particle in the space interval dx in the nth state:

P(n,x)dx = (2/L)sin^2(nπx/L)dx

where L is the width of the well, n is the quantum number, x is the distance from the edge of the well, P(n,x) is the probability of finding an electron in the space interval dx.

Substituting the values, we get:

P(3,0.02l) = (2/l)sin^2(3π(0.02l)/l)dl

P(3,0.02l) = (2/l)sin^2(0.06π)dl

P(3,0.02l) ≈ 0.0206

Thus, the probability of finding an electron in an excited state (n=3) at a distance of 0.02l from the edge of the well is approximately 0.0206.

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This digital product - a problem book "? an electron in an infinitely deep one-dimensional potential well" contains many problems and examples on the topic of quantum mechanics related to the movement of an electron in an infinitely deep one-dimensional rectangular potential well of width l.

One of the tasks that can be found in this problem book is the following: find the probability that an electron in an excited state (n=3) is located at a distance of 0.02l from the edge of the well. To solve this problem, it is necessary to use the formula for the probability of finding a particle in the space interval dx in the nth state:

P(n,x)dx = (2/L)sin^2(nπx/L)dx

where L is the width of the well, n is the quantum number, x is the distance from the edge of the well, P(n,x) is the probability of finding an electron in the space interval dx.

Substituting the values, we get:

P(3,0.02l) = (2/l)sin^2(3π(0.02l)/l)dl P(3,0.02l) = (2/l)sin^2(0.06π)dl P(3,0.02l) ≈ 0.0206

Thus, the probability of finding an electron in an excited state (n=3) at a distance of 0.02l from the edge of the well is approximately 0.0206.

The problem book provides detailed solutions to each problem, as well as step-by-step instructions and tips for solving it. It will be useful to both beginners and experienced students and teachers of quantum mechanics. Our product will help you deepen your knowledge in the field of quantum mechanics and successfully cope with any problems on this topic.

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This product is an image file containing a detailed solution to problem 60524 on the theory of quantum mechanics. The task is to determine the probability of finding an excited electron (n=3) in a one-dimensional rectangular potential well of width l at a distance of 0.02l from the edge of the well.

The file contains a brief statement of the problem, as well as the formulas and laws used, the derivation of the calculation formula and the answer. If you have any questions about solving the problem, the seller promises to help.

Please note that this product is intended for those who are interested in the theory of quantum mechanics and have a sufficient level of knowledge in this field.

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