Consider a particle in the one-dimensional box with the following wave function: (x,0) = Cx(a − x) 4. Normalize this wavefunction. 5. Express &(x, 0) as a superposition of eigenfunctions PE (x). 6. What is the probability of each of these eigenfunctions?
Consider a particle in the one-dimensional box with the following wave function: (x,0) = Cx(a − x) 4. Normalize this wavefunction. 5. Express &(x, 0) as a superposition of eigenfunctions PE (x). 6. What is the probability of each of these eigenfunctions?
Related questions
Question
Transcribed Image Text:Consider a particle in the one-dimensional box with the following wave function:
(x,0) = Cx(a − x)
4. Normalize this wavefunction.
5. Express (x, 0) as a superposition of eigenfunctions (x).
6. What is the probability of each of these eigenfunctions?
7. Verify that the sum of all probabilities in (6) is unity.
Hint: Use
8. When the system is at
9. When the system is at
10. When the system is at
11. When the system is at
12. When the system is at
13. When the system is at
14.What is (x, t)
15. What is (2) ?
dt'
16. What is (d)?
dt
+∞
Σ
n=0
1
(2n + 1)6
(x, 0), what is (x)?
(x, 0), what is (²)?
(x, 0), what is (p)?
(x, 0), what is (p²)?
(x, 0), what is Ax?
(x, 0), what is Ap?
=
π6
960
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 4 images
