To show that the energy of the electron in a three dimensional box of edge length
Answer to Problem 37P
It is showed that the energy of the electron in a three dimensional box of edge length
Explanation of Solution
Write the wave function of the particle given in question.
Here,
The electron moves in a cub of length
Substitute
At boundary the wave function vanishes. Therefore, at
Substitute
Solve above equation for
Solve above equation for
Solve above equation for
Substitute
Write the three dimensional Schrodinger equation for the electron moving in a cubical box of potential
Here,
In the problem, the electron is moving in zero potential.
Substitute
Substitute
Simplify above equation.
Conclusion:
Substitute
Equate the coefficient of above equation to get
Therefore, it is showed that the energy of the electron in a three dimensional box of edge length
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Chapter 43 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
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