(5) The wave funetion for a particle is given by: ý(x) = Ae=/L for z 2 0, where A and L are constants, and L> 0. b(x) = 0 for r < 0. (a) Find the value of the constant A, as a function of L. A useful integral is: ƒe-K=dx = -e-Kz, 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 funetion for a particle is given by: ý(x) = Ae=/L for z 2 0, where A and L are constants, and L> 0. b(x) = 0 for r < 0. (a) Find the value of the constant A, as a function of L. A useful integral is: ƒe-K=dx = -e-Kz, 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 r 2 0, where A and L are constants, and L > 0.
b(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 = -ke-K,
%3D
where K is a constant.
(b) What is the probability of finding the particle in the range –10 L < x< -L?
(c) What is the probability of finding the particle in the range 0 <r< L?
(d) What is the expectation value (r) for the particle, when the particle is in the range 0 < a < L?
A useful integral is: [udv = uv – fvdu.
(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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