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?

International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:Andrew Pytel And Jaan Kiusalaas
Chapter1: Introduction To Statics
Section: Chapter Questions
Problem 1.63P: Let A and B be two nonparallel vectors that lie in a common plane S. If C=A(AB), which of the...
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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
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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