What distinguishes the average and most likely position of a particle?

[TFM]

OKay, well I have:

B^2\left[ -\frac{1}{2\beta}e^{-2\beta x} + frac{3}{2 \beta\left[ -frac{-x^2}{2\beta}e^{-2 \beta x} + \frac{1}{\beta} \left[ \frac{x}{2\beta}e^{-2\beta x} + 1\frac{1}{2\beta} \left[ -\frac{1}{2\beta} e^{-2\beta x} \right]\right] /right]} \right]

Which I have reduced to:

B^2\left[-\frac{x^3}{2\beta}e^{-2\beta x} + \frac(-\frac{3x^2}{4\beta^2}e^{-2\beta x} + \frac{3x}{4\beta^3}e^{-2\beta x} - \frac{3}{8\beta^4}e^{-2 \beta x} \right]

B^2 = 4\beta^2

\left[-\frac{B^2x^3}{2\beta}e^{-2\beta x} - \frac{B^23x^2}{4\beta^2}e^{-2\beta x} + \frac{B^23x}{4\beta^3}e^{-2\beta x} - \frac{3B^2}{8\beta^4}e^{-2 \beta x} \right]

\left[-\frac{4\beta x^3}{2}e^{-2\beta x} - 3x^2e^{-2\beta x} + \frac{3x}{4\beta}e^{-2\beta x} - \frac{3}{2\beta^2}e^{-2 \beta x} \right]

 

[malawi_glenn]

if you want to check your integrals:

http://integrals.wolfram.com/index.jsp

;-)