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I want you to do this assignment in MATLAB. It is about materials and devices. I will upload the the instructions followed by the questions. Please read it carefully. It has to be done in MATLAB, hand calculation and answering questions with explanation. Everything is clear and simple. Also, I will upload a picture of the Grading Rubric.
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With the help of a computer and a commercial software package such as Matlab
solve Schrodinger's Wave Equation (SWE) for the following problem:
1. Consider the particle in the two dimensional infinite potential well as shown in Figure 1.
The width of the well in the x-axis is -L/2«x«L/2 and in the z-axis is O«z«L. The walls of
the well V(x,z) are infinitely high. Do or answer the following.
V(x,z)
z
Figure 1.
(a.)Derive the wave functions (ie. Y.(x2)) corresponding to the four lowest
energy levels. (Show all work for full credit.) (Note: Do not use degenerate
energy levels. No energy level should have the same value.)
(b.) By hand calculations, from (a) and using the separation of variables technique
to show that energy is given by
E = h (n+n), Equation 1
8L m
(Note: Remember to label all axes and DO NOT FORGET UNITS!! Make sure to SHOW ALL WORK!!)
(c.)Use Matlab to calculate the energy of the four lowest energy levels. (Exz).
(Note: 'n' must have whole integer number values (ie. 1,2,3...) (Note: Do not use
degenerate energy levels. No energy level should have the same value.)
(d.) Use Matlab to plot the normalized wave functions (ie. ºn«r2(x,z))) that
correspond to the four lowest energy levels. (Note: Make sure to label your
plots.)
(e.) Is the energy of the particle quantized or continuous? Explain.
(f.) What is the probability of the particle existing at x =0.3 Land z=0.5 L? Assume
L = 1X10-10 meters
Criteria Lab 1 SWE
Points
1.Introduction
5
Assignment
a. Hand calculations to solve SWE Psi(x,z), derivation
b. Hand calculations to derive Energy
30
20
16
16
C. Matlab computation of the four lowest energies,
d. Plot of normalized wave solutions
e. Is energy quanitized or continuous?
f. Probability of finding particle at x =.3L and z = .5L
4
10
2. Discussion of Results/Conclusion
5
3. Presentation
A. Title Page
B. Table of Contents
2
NN
2
110
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Explanation & Answer
Attached.
Running head: ELECTRICAL ENGINEERING
Schrodinger’s Wave Equation
Name
Institution
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ELECTRICAL ENGINEERING
2
...
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