A particle confined in an infinite square well between x = 0 and r = L is prepared with wave function 1/VL if 0< x < L $(x) = otherwise 1. Does the particle have a well-defined energy? 2. What is the probability to find the particle in the n'th bound state n (see Eq. 1.71) that has a well-defined energy En = (Thn/L)²/2m? 3. What is the average energy of the particle? Explain the the requirement that physical wave functions don't have discontinuities, in view of your answer.
A particle confined in an infinite square well between x = 0 and r = L is prepared with wave function 1/VL if 0< x < L $(x) = otherwise 1. Does the particle have a well-defined energy? 2. What is the probability to find the particle in the n'th bound state n (see Eq. 1.71) that has a well-defined energy En = (Thn/L)²/2m? 3. What is the average energy of the particle? Explain the the requirement that physical wave functions don't have discontinuities, in view of your answer.
Related questions
Question
100%
Transcribed Image Text:Problem 1.8
A particle confined in an infinite square well between x = 0 and x = L is
prepared with wave function
de) = {
1/VI
if 0 < x < L
otherwise
1. Does the particle have a well-defined energy?
2. What is the probability to find the particle in the n'th bound state n
(see Eq. 1.71) that has a well-defined energy En = (Tħn/L)²/2m?
3. What is the average energy of the particle? Explain the the requirement
that physical wave functions don't have discontinuities, in view of your
answer.
Problem 1.9
Consider a particle in the n'th bound state ,n(x) (see Eq. 1.71) of an infinite
square well between x = 0 and x = L.
1. Use a symmetry argument to prove that (x) = L/2 where (x) is the
average position computed from the results of many identical experi-
ments.
1.7. PROBLEMS
35
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
