**Problem 1.15 Suppose you wanted to describe an unstable particle, that spon- taneously disintegrates with a "lifetime" t. In that case the total probability of finding the particle somewhere should not be constant, but should decrease at (say) an exponential rate: too P(t) = | V(x, 1)1²dx = e~1/*. A crude way of achieving this result is as follows. In Equation 1.24 we tacitly assumed that V (the potential energy) is real. That is certainly reasonable, but it leads to the "conservation of probability" enshrined in Equation 1.27. What if we assign to V an imaginary part: V = Vo – ir, where Vo is the true potential energy and r is a positive real constant? (a) Show that (in place of Equation 1.27) we now get d P 2Г = -- P dt (b) Solve for P(t), and find the lifetime of the particle in terms of r.
**Problem 1.15 Suppose you wanted to describe an unstable particle, that spon- taneously disintegrates with a "lifetime" t. In that case the total probability of finding the particle somewhere should not be constant, but should decrease at (say) an exponential rate: too P(t) = | V(x, 1)1²dx = e~1/*. A crude way of achieving this result is as follows. In Equation 1.24 we tacitly assumed that V (the potential energy) is real. That is certainly reasonable, but it leads to the "conservation of probability" enshrined in Equation 1.27. What if we assign to V an imaginary part: V = Vo – ir, where Vo is the true potential energy and r is a positive real constant? (a) Show that (in place of Equation 1.27) we now get d P 2Г = -- P dt (b) Solve for P(t), and find the lifetime of the particle in terms of r.
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter5: Analysis Of Convection Heat Transfer
Section: Chapter Questions
Problem 5.8P
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