- #1

- 46

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[tex] \psi (x,t) = Ae^ {-\lambda \mid x\mid}e^ {-(i ) \omega t} [/tex]

where A, [itex] \lambda [/itex], and [itex] \omega [/itex] are positive real constants

I'm asked to find the expectation values of x and x^2.

I know that the values are given by

[tex] <x> = \int_{-\infty}^{+\infty} x(A^2)e^ {-2\lambda \mid x\mid} dx [/tex]

and

[tex] <x^2> = \int_{-\infty}^{+\infty} (x^2)(A^2)e^ {-2\lambda \mid x\mid} dx [/tex]

However, when calculated, I get <x> = <x^2> = 0. Since this would yield a standard deviation of zero, I'm thinking I've made a mistake (the reasoning being that the function does have some spread).

Does this seem correct, or should I be getting a non-zero value for one of the expectation values?