- Kindly Answer Both Parts Of Question 1 (34.06 KiB) Viewed 43 times
Kindly Answer both parts of question
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Kindly Answer both parts of question
Kindly Answer both parts of question
Question 01 (20 points) (a) In the following, three potential wells are given. Make qualitative sketches of possible energy eigenfunctions for the given energy levels. For each case, find out the region where the probability of finding the particle is maximum. Give a brief justification for each sketch Note: Following aspects of the sketch will be marked L == 11. Wavefunction must satisfy the boundary conditions Appropriate depiction of the variation in the frequency and the amplitude of the oscillating part of the wavefunction. Shape of the wavefunction in the classically forbidden regions L(3 pts) (po) o>a 111 00 8 E 00 K a M 0a 0 (b) Consider the infinite potential energy well with a rectangular barrier at the center as shown below. A particle is initially on the left side of the barrier with energy E. Answer the following questions with proper justification E 1221 Nel 976 E 743 (2 points) If the width of the potential barrier is increased as compared to that shown in the above plot, does the probability of tunneling to the right side increase or decrease? (2 points) If the height of the potential barrier is increased as compared to that shown in the above plot, does the probability of tunneling increase or decrease? L (1.5 points) If the energy of the particle is decreased as compared to that shown in the above plot, does the probability of tunneling increase or decrease? de =4136x1077-022
Question 01 (20 points) (a) In the following, three potential wells are given. Make qualitative sketches of possible energy eigenfunctions for the given energy levels. For each case, find out the region where the probability of finding the particle is maximum. Give a brief justification for each sketch Note: Following aspects of the sketch will be marked L == 11. Wavefunction must satisfy the boundary conditions Appropriate depiction of the variation in the frequency and the amplitude of the oscillating part of the wavefunction. Shape of the wavefunction in the classically forbidden regions L(3 pts) (po) o>a 111 00 8 E 00 K a M 0a 0 (b) Consider the infinite potential energy well with a rectangular barrier at the center as shown below. A particle is initially on the left side of the barrier with energy E. Answer the following questions with proper justification E 1221 Nel 976 E 743 (2 points) If the width of the potential barrier is increased as compared to that shown in the above plot, does the probability of tunneling to the right side increase or decrease? (2 points) If the height of the potential barrier is increased as compared to that shown in the above plot, does the probability of tunneling increase or decrease? L (1.5 points) If the energy of the particle is decreased as compared to that shown in the above plot, does the probability of tunneling increase or decrease? de =4136x1077-022