(5) The wave function for a particle is given by: (x) = Ae-/L for r 0, where A and L are constants, and L> 0. (a) 0 for I<0. (a) Find the value of the constant A, as a function of L. A useful integral is: fe-K*dx = -ke-Kr, where K is a constant. (b) What is the probability of finding the particle in the range -10 L < r <-L? (c) What is the probability of finding the particle in the range 0
(5) The wave function for a particle is given by: (x) = Ae-/L for r 0, where A and L are constants, and L> 0. (a) 0 for I<0. (a) Find the value of the constant A, as a function of L. A useful integral is: fe-K*dx = -ke-Kr, where K is a constant. (b) What is the probability of finding the particle in the range -10 L < r <-L? (c) What is the probability of finding the particle in the range 0
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Transcribed Image Text:(5) The wave function for a particle is given by:
(x) = Ae/L for x 0, where A and L are constants, and L>0.
(x) 0 for r <0.
(a) Find the value of the constant A, as a function of L. A useful integral is: fe-K*dx =D-e-K,
where K is a constant.
(b) What is the probability of finding the particle in the range -10 L<r <-L?
(c) What is the probability of finding the particle in the range 0<I< L?
(d) What is the expectation value (x) for the particle, when the particle is in the range 0 <r< L?
A useful integral is: udv=uv-
-Sudu.
(e) Suppose the total energy E of the particle is:
E
2mL2
What is the potential energy of the particle, as a function of m and L? Assume non-relativistic motion.
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