Let P ab (t) be the probability of finding the particle in the range (a < x
Question:
Let Pab (t) be the probability of finding the particle in the range (a < x < b), at time t.
(a) Show that
What are the units of J (x,t)? J is called the probability current because it tells you the rate at which probability is “flowing” past the point x. If is Pab (t) is increasing, then more probability is flowing into the region at one end than flows out at the other.
(b) Find the probability current for the wave function in Problem 1.9. (This is not a very pithy example, I’m afraid; we’ll encounter more substantial ones in due course.)
Problem 1.9.
A particle of mass m has the wave function
where A and a are positive real constants.
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Related Book For
Introduction To Quantum Mechanics
ISBN: 9781107189638
3rd Edition
Authors: David J. Griffiths, Darrell F. Schroeter
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