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1. Consider a particle of mass m which can move freely along the x axis anywhere from x = -a/2 to x = a/2, but which is strictly prohibited from being found outside this region. The particle is described by the wavefunction Y((x, t) = = Acos()e-Et/h, if -a/2 < x, +a/2 a otherwise 10, (i) Does V(x, t) verify the Schrödinger's Equation? (ii) Determine the probability density P(x, t). (iii) Docs (x, t) verify the Born's postulate? (iv) Does V(x, t) verify Heisenberg's Uncertainty Principle?

1. Consider a particle of mass m which can move freely along the x axis anywhere from x = -a/2 to x = a/2, but which is strictly prohibited from being found outside this region. The particle is described by the wavefunction Y((x, t) = = Acos()e-Et/h, if -a/2 < x, +a/2 a otherwise 10, (i) Does V(x, t) verify the Schrödinger's Equation? (ii) Determine the probability density P(x, t). (iii) Docs (x, t) verify the Born's postulate? (iv) Does V(x, t) verify Heisenberg's Uncertainty Principle?

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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X 1. Consider a particle of mass m which can move freely along the x axis anywhere from x = -a/2 to x = a/2, but which is strictly prohibited from being found outside this region. The particle is described by the wavefunction Acos(T)e-iEt/h, if -a/2<x, +a/2 V ((x, t) 0, otherwise (i) Does V(x, t) verify the Schrödinger's Equation? (ii) Determine the probability density P(x, t). (iii) Does (x, t) verify the Born's postulate? (iv) Does V(x, t) verify Heisenberg's Uncertainty Principle?
Transcribed Image Text:X 1. Consider a particle of mass m which can move freely along the x axis anywhere from x = -a/2 to x = a/2, but which is strictly prohibited from being found outside this region. The particle is described by the wavefunction Acos(T)e-iEt/h, if -a/2<x, +a/2 V ((x, t) 0, otherwise (i) Does V(x, t) verify the Schrödinger's Equation? (ii) Determine the probability density P(x, t). (iii) Does (x, t) verify the Born's postulate? (iv) Does V(x, t) verify Heisenberg's Uncertainty Principle?
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