Let Y(x, t) = Aee, where 0 ‡ A € C, E and L> 0 are constants.(a) Is (x, t) an acceptable wavefunction? Explain.(b) Find A so that Y(x, t) is normalized.(c) Show that (x, 1)² = |¥(x,0)|² Vt.

Answered: Let Y(x, t) = Aee, where 0 A € C, E and…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let Y(x, t) = Aee, where 0 ‡ A € C, E and L> 0 are constants.
(a) Is (x, t) an acceptable wavefunction? Explain.
(b) Find A so that Y(x, t) is normalized.
(c) Show that (x, 1)² = |¥(x,0)|² Vt.

Expert Solution

Step 1

The scalar function $f (x, t)$ is a rule that associates or fixes a number to a particular point x at a particular time t. In this problem, the given function is $Ψ (x, t) \equiv A e^{- \frac{|x|}{L}} e^{- \frac{i E t}{h}}$ , where $0 \neq A \in ℂ, E$ and $L > 0$ . In the first part of the problem, we have to check where $Ψ (x, t)$ is an acceptable function. In the second part, we have to find the value of A so that $Ψ (x, t)$ is normalized. In the third part, we have to show that ${|Ψ (x, t)|}^{2} = {|Ψ (x, 0)|}^{2}$ .