The average position,or expectation value,of a particle whose wave function$\Psi$(x)depends only on the value of x,is given by = A) $\int _ { - \infty } ^ { + \infty } \sqrt { x } \psi ( x ) d x$ . B) $\int _ { - \infty } ^ { + \infty } x \psi ( x ) d x$ . C) $\int _ { - \infty } ^ { + \infty } \frac { x } { 2 } \psi ^ { 2 } ( x ) d x$ . D) $\int _ { - \infty } ^ { + \infty } \frac { x ^ { 2 } } { 2 } \psi ( x ) d x$ . E) $\int _ { - \infty } ^ { + \infty } \psi ^ { * } ( x ) x \psi ( x ) d x$ .

Question

The average position,or expectation value,of a particle whose wave function$\Psi$(x)depends only on the value of x,is given by < x > =
A) $\int _ { - \infty } ^ { + \infty } \sqrt { x } \psi ( x ) d x$ .
B) $\int _ { - \infty } ^ { + \infty } x \psi ( x ) d x$ .
C) $\int _ { - \infty } ^ { + \infty } \frac { x } { 2 } \psi ^ { 2 } ( x ) d x$ .
D) $\int _ { - \infty } ^ { + \infty } \frac { x ^ { 2 } } { 2 } \psi ( x ) d x$ .
E) $\int _ { - \infty } ^ { + \infty } \psi ^ { * } ( x ) x \psi ( x ) d x$ .

Quizplus · Accepted Answer

The expectation value of position <x> for a wave function $\psi(x)$ is given by $\int _ { - \infty } ^ { + \infty } \psi ^ { * } ( x ) x \psi ( x ) d x$, where $\psi^*(x)$ is the complex conjugate of the wave function.

The Average Position,or Expectation Value,of a Particle Whose Wave Function Ψ\PsiΨ

The Average Position,or Expectation Value,of a Particle Whose Wave Function $\Psi$