- #1
Radarithm
Gold Member
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Homework Statement
Consider the wave function $$\Psi(x,t)=Ae^{-\lambda|x|}e^{-i\omega t}$$
Where ##A##, ##\lambda##, and ##\omega## are positive real constants.
(a)Normalize ##\Psi##.
(b)Determine expectation values of ##x## and ##x^2##.
Homework Equations
$$\int_{-\infty}^{+\infty}|\Psi(x,t)|^2dx=\int_{-\infty}^{+\infty}\Psi\Psi^{\ast}dx=1$$
The Attempt at a Solution
Correct me if I'm wrong, but in order to normalize the wave function you need to re-write A in terms of the other constants and ##x##, and normalize it at t = 0. This is what I did:
$$\int_{-\infty}^{+\infty}|\Psi(x,0)|^2dx$$
$$|A|^2\int_{-\infty}^{+\infty}e^{-\lambda^2|x|^2}dx$$
$$|A|^2\frac{\sqrt{\pi}}{2\lambda}=1$$
$$A=\frac{\sqrt{2\lambda}}{(\pi^{1/4})}$$
Did I go wrong somewhere in (a) ?