Given the wave function:(adsbygoogle = window.adsbygoogle || []).push({});

[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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Expectation values of x and x^2

**Physics Forums | Science Articles, Homework Help, Discussion**