- #1
cyberdeathreaper
- 46
- 0
Given the wave function:
[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?
[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?