0 1/31 1/30 0 1/3Numerically verify that each initial state vector xo has the given steady-state vector x.[0.5750.42500.681Let A = 0Xo = 0.270.310.49X1x₁ = 0.130.38Axo =0.421A4x0 =A³xo =⇒0.320Ax₁ =841A4x₁ =A³x₁ =

Answered: 0 1/3 1 1/3 00 1/3 Numerically verify…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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3.12 Let E, denote the bound-state energy eigenvalues of a one-dimensional system and let yn(x) denote the corresponding energy eigenfunctions. Let ¥(x, 1) be the wave function of the system, normalised to unity, and suppose that at t = 0 it is given by 1 giaii(x) + 1 :el":V2(x) + 1 iaz e"V3(x) ¥(x,1 = 0) = where the a; are real constants. (a) Write down the wave function ¥(x, 1) at time t. (b) Find the probability that at time t a measurement of the energy of the system gives the value E2. (c) Does (x) vary with time? Does (px) vary with time? Does E = (H) vary with time?
1 0 1/3 0 1 1/3 0 0 1/3 Numerically verify that each initial state vector xo has the given steady-state vector x. 0.42 0.575 xo= 0.27 0.425 0.31 0 0.49 0.68 0.13 0.32 0.38 0 Let A = X1 ⇒> x₁ = Axo = Axo = Axo = E Ax₁ = A¹x₁ = A³x₁ = =
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0 1/3 1 1/3 00 1/3 Numerically verify that each initial state vector xo has the given steady-state vector x. 0.575 0.425 0 0.68 Let A = 0.42 Xo = 0.27 0.31 0.49 X1 = 0.13 0.38 Axo = A4x0 = 1 0 A³x0 = 0.32 0 Ax₁ = A¹x₁ = A³x₁ =